1Cademy - Solving $$-4(a - 3) - 7 = 25$$ by Distributing and Simplifying

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Example

Solving $-4(a - 3) - 7 = 25$ by Distributing and Simplifying

To solve the equation $-4(a - 3) - 7 = 25$ , the left side must first be simplified using the distributive property and by combining like terms before the variable can be isolated.

Step 1 — Distribute: Multiply $-4$ by each term inside the parentheses: $-4 \cdot a = -4a$ and $-4 \cdot (-3) = 12$ (two negatives produce a positive). The equation becomes:

$-4a + 12 - 7 = 25$

Step 2 — Combine like terms: The constants $12$ and $-7$ on the left side are like terms: $12 - 7 = 5$ . The equation simplifies to:

$-4a + 5 = 25$

Step 3 — Subtract $5$ from both sides: Apply the Subtraction Property of Equality to isolate the variable term:

$-4a + 5 - 5 = 25 - 5$

$-4a = 20$

Step 4 — Divide both sides by $-4$ : Apply the Division Property of Equality. Because $a$ is multiplied by the negative coefficient $-4$ , divide both sides by $-4$ :

$\frac{-4a}{-4} = \frac{20}{-4}$

$a = -5$

Step 5 — Check by substitution: Replace $a$ with $-5$ in the original equation:

$-4(-5 - 3) - 7 \stackrel{?}{=} 25$

$-4(-8) - 7 \stackrel{?}{=} 25$

$32 - 7 \stackrel{?}{=} 25$

$25 = 25 \checkmark$

Because both sides are equal, $a = -5$ is confirmed as the correct solution. This example illustrates how distributing a negative factor and combining constants are necessary simplification steps before the Division Property of Equality can be applied to solve for the variable.

Updated 2026-04-21

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OpenStax Elementary Algebra

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