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Simplifying 4(q + -6) + -3q + 2q = 5(10 + 3q) + 22 Reorder the terms: 4(-6 + q) + -3q + 2q = 5(10 + 3q) + 22 (-6 * 4 + q * 4) + -3q + 2q = 5(10 + 3q) + 22 (-24 + 4q) + -3q + 2q = 5(10 + 3q) + 22 Combine like terms: 4q + -3q = 1q -24 + 1q + 2q = 5(10 + 3q) + 22 Combine like terms: 1q + 2q = 3q -24 + 3q = 5(10 + 3q) + 22 -24 + 3q = (10 * 5 + 3q * 5) + 22 -24 + 3q = (50 + 15q) + 22 Reorder the terms: -24 + 3q = 50 + 22 + 15q Combine like terms: 50 + 22 = 72 -24 + 3q = 72 + 15q Solving -24 + 3q = 72 + 15q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-15q' to each side of the equation. -24 + 3q + -15q = 72 + 15q + -15q Combine like terms: 3q + -15q = -12q -24 + -12q = 72 + 15q + -15q Combine like terms: 15q + -15q = 0 -24 + -12q = 72 + 0 -24 + -12q = 72 Add '24' to each side of the equation. -24 + 24 + -12q = 72 + 24 Combine like terms: -24 + 24 = 0 0 + -12q = 72 + 24 -12q = 72 + 24 Combine like terms: 72 + 24 = 96 -12q = 96 Divide each side by '-12'. q = -8 Simplifying q = -8
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