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Simplifying 7(-4q + 12) + -14q = 6(-8q + 19) Reorder the terms: 7(12 + -4q) + -14q = 6(-8q + 19) (12 * 7 + -4q * 7) + -14q = 6(-8q + 19) (84 + -28q) + -14q = 6(-8q + 19) Combine like terms: -28q + -14q = -42q 84 + -42q = 6(-8q + 19) Reorder the terms: 84 + -42q = 6(19 + -8q) 84 + -42q = (19 * 6 + -8q * 6) 84 + -42q = (114 + -48q) Solving 84 + -42q = 114 + -48q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '48q' to each side of the equation. 84 + -42q + 48q = 114 + -48q + 48q Combine like terms: -42q + 48q = 6q 84 + 6q = 114 + -48q + 48q Combine like terms: -48q + 48q = 0 84 + 6q = 114 + 0 84 + 6q = 114 Add '-84' to each side of the equation. 84 + -84 + 6q = 114 + -84 Combine like terms: 84 + -84 = 0 0 + 6q = 114 + -84 6q = 114 + -84 Combine like terms: 114 + -84 = 30 6q = 30 Divide each side by '6'. q = 5 Simplifying q = 5
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