1Cademy - Solving $$-(y + 9) = 8$$ by Distributing $$-1$$

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Strategy for Solving Linear Equations

Example

Solving $-(y + 9) = 8$ by Distributing $-1$

To solve the equation $-(y + 9) = 8$ , recognize that the negative sign in front of the parentheses means the expression is being multiplied by $-1$ , then apply the general strategy for linear equations.

Step 1 — Distribute $-1$ : Multiply $-1$ by each term inside the parentheses: $-1 \cdot y = -y$ and $-1 \cdot 9 = -9$ . The equation becomes:

$-y - 9 = 8$

Step 2 — Add $9$ to both sides: The variable term $-y$ is already on the left, so use the Addition Property of Equality to move the constant $-9$ to the right:

$-y - 9 + 9 = 8 + 9$

$-y = 17$

Step 3 — Rewrite $-y$ as $-1y$ and divide by $-1$ : The expression $-y$ is equivalent to $-1 \cdot y$ . Dividing both sides by $-1$ isolates the variable:

$\frac{-1y}{-1} = \frac{17}{-1}$

$y = -17$

Step 4 — Check by substitution: Replace $y$ with $-17$ in the original equation:

$-(-17 + 9) \stackrel{?}{=} 8$

$-(-8) \stackrel{?}{=} 8$

$8 = 8 \checkmark$

Because both sides are equal, $y = -17$ is confirmed as the correct solution. The key insight in this problem is that a bare negative sign in front of parentheses is an implicit multiplication by $-1$ . A related technique appears when isolating $-y$ : rewriting it explicitly as $-1y$ makes clear that dividing both sides by $-1$ is the operation needed to produce a coefficient of $1$ .

Updated 2026-04-21

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OpenStax Elementary Algebra

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