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Full access to solution steps Full access to AI chat Practice and improve Access from any device Unlimited storage Detect AI-generated content Advanced Grammar Checker Paraphrase in unlimited modes Summarize any text Back to School Promotion qb-banner-title Equations Basic (Linear) One-Step Addition One-Step Subtraction One-Step Multiplication One-Step Division One-Step Decimals Two-Step Integers Two-Step Add/Subtract Two-Step Multiply/Divide Two-Step Fractions Two-Step Decimals Multi-Step Integers Multi-Step with Parentheses Multi-Step Rational Multi-Step Fractions Multi-Step Decimals Solve For Quadratic Solve by Factoring Completing the Square Quadratic Formula Rational Biquadratic Polynomial Radical Logarithmic Exponential Absolute Complex Matrix Roots Zeroes Rational Roots Floor/Ceiling Equation Given Roots Equation Given Points Newton Raphson Basic (Linear) One-Step Addition One-Step Subtraction One-Step Multiplication One-Step Division One-Step Decimals Two-Step Integers Two-Step Add/Subtract Two-Step Multiply/Divide Two-Step Fractions Two-Step Decimals Multi-Step Integers Multi-Step with Parentheses Multi-Step Rational Multi-Step Fractions Multi-Step Decimals One-Step Addition One-Step Subtraction One-Step Multiplication One-Step Division One-Step Decimals Two-Step Integers Two-Step Add/Subtract Two-Step Multiply/Divide Two-Step Fractions Two-Step Decimals Multi-Step Integers Multi-Step with Parentheses Multi-Step Rational Multi-Step Fractions Multi-Step Decimals Quadratic Solve by Factoring Completing the Square Quadratic Formula Solve by Factoring Completing the Square Quadratic Formula Equation Given Roots Equation Given Points Inequalities Linear Quadratic Absolute Radical Rational Logarithmic Exponential Compound System of Equations Linear Substitution Elimination Cramer's Rule Gaussian Elimination Non Linear Linear Substitution Elimination Cramer's Rule Gaussian Elimination Gaussian Elimination System of Inequalities Testing Solutions Basic Operations Simplify Factoring GCF Trinomials Grouping Perfect Squares Difference of Squares Difference of Cubes Sum of Cubes Polynomials Factor Completely Expand Distributive Property FOIL method Difference of Squares Perfect Squares Perfect Cubes Trinomials Binomial Expansion Join Cancel Factoring GCF Trinomials Grouping Perfect Squares Difference of Squares Difference of Cubes Sum of Cubes Polynomials Factor Completely Perfect Squares Difference of Squares Difference of Cubes Factor Completely Expand Distributive Property FOIL method Difference of Squares Perfect Squares Perfect Cubes Trinomials Binomial Expansion Distributive Property Difference of Squares Perfect Squares Binomial Expansion Algebraic Properties Exponents Zero Rule Negative Rule Product Rule Quotient Rule Power Rule Expand Power Rule Fraction Exponent Exponent Rules Exponential Form Logarithms One Rule Power Rule Product Rule Quotient Rule Expand Condense Base 2 Properties Logarithmic Form Radicals Product Rule Quotient Rule Multiply Divide Reduce Absolute Value Factorial Rational Number Complex Numbers Powers of i Multiply Divide Conjugate Magnitude A+Bi Form Complex Form Floor Ceiling LCD GCD Exponents Zero Rule Negative Rule Product Rule Quotient Rule Power Rule Expand Power Rule Fraction Exponent Exponent Rules Exponential Form Expand Power Rule Fraction Exponent Exponential Form Logarithms One Rule Power Rule Product Rule Quotient Rule Expand Condense Base 2 Properties Logarithmic Form Radicals Product Rule Quotient Rule Multiply Divide Reduce Rational Number Complex Numbers Powers of i Multiply Divide Conjugate Magnitude A+Bi Form Complex Form Partial Fractions Polynomials Properties Is Polynomial Leading Coefficient Leading Term Degree Standard Form Prime Add Subtract Multiply Divide Factor Complete the Square Synthetic Division Ruffini Method LCM GCD Linear Factors Properties Is Polynomial Leading Coefficient Leading Term Degree Standard Form Prime Leading Coefficient Complete the Square Synthetic Division Rational Expressions Add Subtract Multiply Divide Reduce Rationalize Rationalize Denominator Rationalize Numerator Rationalize Rationalize Denominator Rationalize Numerator Rationalize Denominator Rationalize Numerator Sequences Identify Type First Term N-th Term Term Index Next Term Specific Term Sum Convergence Alternating Sequence Sum Arithmetic Geometric Constant General Alternating Sequence Sum Interval Notation Pi (Product) Notation Logical Sets Boolean Algebra Truth Table Set Theory Intersect Union Difference Subset Mutual Exclusive Cardinality Powerset Caretesian Product Boolean Algebra Mutual Exclusive Caretesian Product Word Problems Age Problems Distance Problems Cost Problems Investment Problems Number Problems Percent Problems Addition/Subtraction Multiplication/Division Probability Problems Dice Problems Coin Problems Card Problems Geometry Circle Square Rectangle Triangle Distance Problems Investment Problems Number Problems Percent Problems Addition/Subtraction Multiplication/Division Probability Problems Dice Problems Coin Problems Card Problems Geometry Circle Square Rectangle Triangle (x+5)(x-5)\gt 0 6+11x+6x^2+x^3=0 factor\:x^{2}-5x+6 simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4} x+2y=2x-5,\:x-y=3 Algebra Calculator: Step-by-Step help to solve Algebra problems Have you ever tried to assemble a jigsaw puzzle with missing pieces and pondered how to find which pieces fit where? Welcome into the realm of algebra! In an amazing mathematical puzzle, letters and symbols take place of unknown numbers. This fundamental branch of mathematics helps us to apply mathematical equations and formulas to visually represent real-world problems. Algebra is there to assist you in everything from determining your monthly budget to calculating how long it takes to get anywhere to even developing a computer program. Origin of Algebra: Algebra originated in ancient Egypt and Babylonia. Algebra comes from an Arabic term meaning "restoration" or "completion." Often credited with giving algebra its name, Diophantus in Greece, Brahmagupta in India, and al-Khwarizmi in Baghdad made significant contributions. What is algebra? Algebra, then, is essentially a branch of mathematics focused on variables , symbols and their operations under guidelines. Mostly letters x, y, and z, these symbols—which stand for quantities without set values—are called variables. Algebra provides general formulas and lets us solve problems for many distinct values. Fundamental Concepts: Variables : Symbols that represent changeable or unknown numbers. Constants : Fixed values that do not change. Expressions : Integration of variables, constants, and operations—like addition and multiplication. Equations : Mathematical statements that show the equality of two expressions constitute equations. Understanding Variables and Constants Variables are like empty boxes that can hold any number. They're placeholders for values we don't know yet or that can change. Example : In the expression $5x+3$, x is a variable. Constants are numbers that have a fixed value. Example : In the same expression 5x+3, 3 is a constant. Variables and constants work together in expressions and equations to model real-world situations. The Language of Algebra Algebra has its own language and symbols: Operations : Addition (+), subtraction (−), multiplication (× or implied by juxtaposition), and division (÷ or /). Coefficients : Numbers multiplied by variables. In 5x, 5 is the coefficient. Terms : The parts of an expression separated by addition or subtraction. In 3x+2, 3x and 2 are terms. Solving algebraic problems would require understanding this language.

Simplification of Algebraic Expressions Why Simplify Expressions? Simplifying expressions helps one to grasp and work with them. It combines similar terms and applies mathematical concepts to create as simple expressions as possible. Combining Like Terms Like terms are terms that have the same variables with same exponents. Example : 7x and 3x are like terms because they both contain x. Combine Like Terms : Identify like terms in the expression. Add or subtract the coefficients of like terms. Rewrite the expression with combined terms. Simplify 4x+5−2x+3. Combine the like terms (4x and −2x): 4x−2x=2x. Combine constants (5 and 3; 5 + 3 = 8). Rewrite the simplified expression: 2x+8. Distributive Property The distributive property of multiplication helps you to remove parentheses. Distributive Property Formula: a(b+c) = ab+ac 1.Multiply the term outside the parentheses by each term inside. 2.Simplify the resulting expression by combining like terms if necessary. Simplify 3(2x + 4). a. Multiply 3 to each term inside the parentheses: b. Multiply: 6x + 12 Simplifying Complex Expressions For expressions with multiple parentheses and terms, use the distributive property to multiply the terms or the constants with the terms given inside the parentheses then combine like terms step by step. Simplify 3(x+2) + 5(x−1). Multiply 3 to each term inside the first set of parentheses: x + 3. 2 = 3x + 6 Multiply 3 to each term inside the first set of parentheses: x + 3. 2 = 3x + 6 Multiply 5 to each term inside the second set of parentheses: x – 5. 1 = 5x − 5 Multiply 5 to each term inside the second set of parentheses: x – 5. 1 = 5x − 5 Combine the results: 3x + 6 + 5x − 5 Combine the results: 3x + 6 + 5x − 5 Combine like terms: (3x + 5x) + (6 − 5) = 8x + 1 Combine like terms: (3x + 5x) + (6 − 5) = 8x + 1 So, 3(x + 2) + 5(x − 1) simplifies to 8x + 1. Solving Algebraic Equations What's an equation? An equation refers to the mathematical statement that represents the balance between two expressions' equality, made with an equals sign (=). Solving an equation is determining the value(s) of the variables that satisfy it. Objective of Solving Equations The main objective is to separate the variable on one side of the equation to find its value. Solving One-Step Equations Addition or Subtraction Equations Example : Solve x+8=12. Subtract 8 from both sides: x=12−8 Multiplication or Division Equations Example : Solve 4x=24. Divide both sides by 4: x = 24 ÷ 4. Solving Two-Step Equations 1.Add 5 to both sides: 4x=12. 2.Divide both sides by 4: x=3 Solving Multi-Step Equations Solve 7(x−2)+3=10. 1.Distribute: 7x−14+3=10. 2.Combine like terms: 7x−11=10. 3.Add 11 to both sides: 7x=21. 4.Divide by 7: x=3. Solving equations with variables on both sides Solve 5x+2=x+10. 1.Subtract x from both sides: 5x−x+2=10. 2.Simplify: 4x+2=10. 3.Subtract 2 from both sides: 4x = 8. 4.Divide by 4 on both sides: x = 2. Verifying the Solution Substitute your solution into the original equation to verify that it satisfies the equation. Check: Does 5(2)+2=2+10? Left Side: 10+2=12 Right Side: 12=12 Both sides are equal, so x=2 is correct. Understanding Inequalities What Are Inequalities? An inequality refers to the comparison of two expressions and represents that one is greater than, less than, greater than or equal to, or less than or equal to the other. Inequality Symbols : > : Greater than ≥ : Greater than or equal to ≤ : Less than or equal to Solving Inequalities When multiplying or dividing both sides of an inequality by a negative number, remember to check and reverse the direction of the inequality sign. Solving inequalities is like solving equations. Solve 2x − 5 < 9. 1.Add 5 to both sides: 2x < 14. 2.Divide both sides by 2: x < 7. 3.Solution: All real numbers less than 7. Special Rule: multiplying or dividing by negative numbers 1.Divide both sides by −3 and reverse the inequality sign: x < −3. 2.Solution: All real numbers less than −3. Algebra in the Real World Solving Word Problems Translating real-world situations into algebraic expressions or equations allows us to solve problems efficiently. A movie theatre charges ​ 10 for adults and ​ 8. If the theatre sells 250 tickets for a total of ​ 1,050, what is the number of adult tickets sold? Let a be the number of adult tickets and c the number of child tickets. Let a be the number of adult tickets and c the number of child tickets. Set up equations: Set up equations: Total tickets: a + c = 250. Total sales: 10a + 8c = 1,050. Solve the system using substitution or elimination. Simplify the solution. Use the Algebra Calculator to solve algebraic equations. Make Math Easier The Algebra Calculator is an adaptable online tool designed to simplify algebraic problem- compatible to solve the problems for all levels of users. Here's how to make the most of it: Begin by entering the algebraic expression into the above input field or upload the image of the problem. After entering the equation, click the 'Go' button to generate instant solutions. The calculator provides detailed step-by-step solutions, aiding in understanding the underlying concepts. How to Use an Algebra Calculator Enter Your Problem : Type in your equation, expression, or system into the calculator's input field. Select the operation : Choose the function you need: solve, simplify , factor , graph , etc. Click Calculate : The calculator processes your input and provides a detailed solution. Review the Steps : The step-by-step explanation helps you understand the process and learn how to solve similar problems. Problem: Solve 5x - 6 = 3x - 8. Calculator Solution: Move 6 to the right side—> 5x = 3x - 2 Move 3x to the left side—> 2x = -2 Divide both sides by -2—> x = -1 Benefits of Using an Algebra Calculator Saves Time : Resolves complex problems. Enhances Learning : Steps that are specific help people understand. Accessible Anywhere : Use it on any device with internet access. Boosts Confidence : Check your work and work on your problem-solving skills. Mastering algebra simplifies the world, despite its initial appearance as a confusing network of symbols and equations. Algebra is the language of describing the workings of everything from financial calculations to engineering marvels. Gain access to limitless opportunities by developing strong analytical skills through regular practice, mastery of the fundamentals, and the use of useful tools such as our Algebra Calculator. Remember, even the most experienced professionals began their journey much later. Discover the captivating realm of algebra by embracing its challenges, remaining persistent, and savoring the ride! How do you solve algebraic expressions? To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true. What are the basics of algebra? The basics of algebra are the commutative, associative, and distributive laws. What are the 3 rules of algebra? The basic rules of algebra are the commutative, associative, and distributive laws. What is the golden rule of algebra? The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too. What are the 5 basic laws of algebra? The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law. algebra-calculator High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,... Please add a message. Message received. Thanks for the feedback.