1Cademy - Solving $$5(a - 3) + 5 = -10$$ by Distributing and Combining Like Terms

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Strategy for Solving Linear Equations

Example

Solving $5(a - 3) + 5 = -10$ by Distributing and Combining Like Terms

To solve the equation $5(a - 3) + 5 = -10$ , begin by simplifying the left side before isolating the variable.

Step 1 — Distribute: Multiply $5$ by each term inside the parentheses: $5 \cdot a = 5a$ and $5 \cdot (-3) = -15$ . The equation becomes:

$5a - 15 + 5 = -10$

Step 2 — Combine like terms: On the left side, the constants $-15$ and $5$ are like terms: $-15 + 5 = -10$ . The equation simplifies to:

$5a - 10 = -10$

Step 3 — Add $10$ to both sides: Use the Addition Property of Equality to move the constant $-10$ to the right side:

$5a - 10 + 10 = -10 + 10$

$5a = 0$

Step 4 — Divide both sides by $5$ : Apply the Division Property of Equality to make the coefficient equal to $1$ :

$\frac{5a}{5} = \frac{0}{5}$

$a = 0$

Step 5 — Check by substitution: Replace $a$ with $0$ in the original equation:

$5(0 - 3) + 5 \stackrel{?}{=} -10$

$5(-3) + 5 \stackrel{?}{=} -10$

$-15 + 5 \stackrel{?}{=} -10$

$-10 = -10 \checkmark$

Because both sides are equal, $a = 0$ is confirmed as the correct solution. This example reinforces that $0$ is a perfectly valid solution to an equation — when the constant terms on the right side cancel completely after isolating the variable term, dividing any coefficient into $0$ always yields $0$ .

Updated 2026-04-21

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OpenStax Elementary Algebra

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