Question

Solve each equation. $$ 7 a+2=12-4(a-3) $$

   Solve each equation.
$$
7 a+2=12-4(a-3)
$$

Intermediate Algebra

Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 1, Problem 70

Instant Answer

Solved by Expert Mitchell Cutler

08/01/2020

Step 1

Step 1: First, we distribute the 4 to the terms inside the parentheses on the right side of the equation: $$ 7a+2=12-4(a-3) \Rightarrow 7a+2=12-4a+12 $$ Show more…

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Solve each equation. $$ 7 a+2=12-4(a-3) $$

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Key Concepts

Isolating the Variable

Isolating the variable involves using inverse operations to rearrange the equation so that the variable appears on one side by itself. This process is fundamental to solving equations as it leads directly to determining the value of the variable.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable parts, which simplifies an equation by reducing the number of terms. This step is essential for consolidating the equation into a simpler form that is easier to solve.

Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised only to the first power. Solving a linear equation involves finding the value of the variable that makes the equation true through a series of algebraic manipulations.

Distributive Property

The distributive property is a fundamental rule in algebra that allows one to multiply a term outside of the parentheses by each term inside the parentheses. This property is crucial for expanding expressions and simplifying equations that involve parentheses.

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