1Cademy - Simplifying $$6(x - 9) - (x + 12)$$ by Distributing and Combining Like Terms

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Simplifying $4(x - 8) - (x + 3)$ by Distributing and Combining Like Terms

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Simplifying $6(x - 9) - (x + 12)$ by Distributing and Combining Like Terms

To simplify the expression $6(x - 9) - (x + 12)$ , the distributive property must be applied to both sets of parentheses before combining like terms.

Step 1 — Distribute both factors: For the first group, multiply $6$ by each term: $6 \cdot x = 6x$ and $6 \cdot 9 = 54$ . For the second group, the negative sign acts as multiplying by $-1$ , which flips the signs of the terms inside: $-1 \cdot x = -x$ and $-1 \cdot 12 = -12$ . The expression becomes: $6x - 54 - x - 12$

Step 2 — Combine like terms: Group the variable terms and the constant terms separately. The $x$ -terms are $6x$ and $-x$ , which combine to $6x - x = 5x$ . The constants are $-54$ and $-12$ , which combine to $-54 - 12 = -66$ : $5x - 66$

This process illustrates how multiple distributions, including one with an implicit $-1$ , prepare a complex algebraic expression for final simplification.

Updated 2026-05-02

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OpenStax Intermediate Algebra

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