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Equivalent Expressions

Study Guide

Key Definition

Equivalent expressions are expressions that have the same value for all values of the variables. They simplify to the same expression.

Important Notes

  • Equivalent expressions simplify to the same value regardless of the variables.
  • Combining like terms is a common method for simplifying expressions.
  • Use the distributive property to simplify expressions.
  • Check equivalency by substituting values for variables.
  • Expressions with different forms can still be equivalent.

Mathematical Notation

$+$ represents addition$-$ represents subtraction$\times$ represents multiplication$\div$ represents division$x^2$ represents x squaredRemember to use proper notation when solving problems

Why It Works

The distributive property and combining like terms preserve the value of an expression, ensuring that rewritten expressions remain equivalent.

Remember

Use substitution to check if expressions are equivalent and apply the distributive property and combining like terms for simplification.

Quick Reference

Distributive Property:$a(b + c) = ab + ac$Combining Like Terms:$2x + 3x = 5x$

Understanding Equivalent Expressions

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

Equivalent expressions are expressions that simplify to the same value. For example, $3 \times 4$ and $6 + 6$ both equal 12.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Which of the following expressions is equivalent to $2x + 3x$?

A$5x$B$6x$C$8x$D$10x$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

You are buying $3$ notebooks and each costs $2x + 1$ dollars. Write an expression for the total cost.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Prove that $4(x + 2) - 3x$ is equivalent to $x + 8$.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Which expression is equivalent to $(x + 3)^2$?

A$x^2 + 6x + 9$B$x^2 + 9$C$x^2 + 5x + 6$D$x^2 + 3x + 3$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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