Question

Solve each equation. $$ -2(3 x+5)=-3(4 x+3) $$

Name: Problem 41, Chapter 2: Intermediate Algebra
Uploaded: 2022-03-28T18:19:54-08:00
Duration: 1 min 56 s
Channel: Debasish Das
Description: Solve each equation. -2(3 x+5)=-3(4 x+3)

   Solve each equation.
$$
-2(3 x+5)=-3(4 x+3)
$$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 2, Problem 41

Instant Answer

Solved by Expert Debasish Das

03/28/2022

Step 1

This gives us: $$ -2(3x+5) = -6x -10 $$ and $$ -3(4x+3) = -12x -9 $$ So the equation becomes: $$ -6x -10 = -12x -9 $$ Show more…

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Solve each equation. $$ -2(3 x+5)=-3(4 x+3) $$

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Key Concepts

Distributive Property

The distributive property is used to eliminate parentheses by multiplying a single term with each term inside the parentheses. This simplifies expressions and is essential in setting up an equation for combining like terms.

Combining Like Terms

Combining like terms involves grouping and simplifying expressions that have the same variable parts in order to reduce the equation to a simpler form, which helps in isolating the variable.

Inverse Operations

Inverse operations are used to reverse operations applied to the variable. These include operations such as addition versus subtraction or multiplication versus division, and are fundamental for isolating and solving for the variable.

Balancing Equations

Balancing equations means performing the same operations on both sides of the equation to maintain equality throughout the solving process. This concept is crucial for transforming and eventually solving the equation.

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