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Simplifying -42 = 5(2c + 9) + -3(c + 8) Reorder the terms: -42 = 5(9 + 2c) + -3(c + 8) -42 = (9 * 5 + 2c * 5) + -3(c + 8) -42 = (45 + 10c) + -3(c + 8) Reorder the terms: -42 = 45 + 10c + -3(8 + c) -42 = 45 + 10c + (8 * -3 + c * -3) -42 = 45 + 10c + (-24 + -3c) Reorder the terms: -42 = 45 + -24 + 10c + -3c Combine like terms: 45 + -24 = 21 -42 = 21 + 10c + -3c Combine like terms: 10c + -3c = 7c -42 = 21 + 7c Solving -42 = 21 + 7c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7c' to each side of the equation. -42 + -7c = 21 + 7c + -7c Combine like terms: 7c + -7c = 0 -42 + -7c = 21 + 0 -42 + -7c = 21 Add '42' to each side of the equation. -42 + 42 + -7c = 21 + 42 Combine like terms: -42 + 42 = 0 0 + -7c = 21 + 42 -7c = 21 + 42 Combine like terms: 21 + 42 = 63 -7c = 63 Divide each side by '-7'. c = -9 Simplifying c = -9
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