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Simplifying 0.5(-12c + 6) = -3(c + 4) + 10(c + -5) Reorder the terms: 0.5(6 + -12c) = -3(c + 4) + 10(c + -5) (6 * 0.5 + -12c * 0.5) = -3(c + 4) + 10(c + -5) (3 + -6c) = -3(c + 4) + 10(c + -5) Reorder the terms: 3 + -6c = -3(4 + c) + 10(c + -5) 3 + -6c = (4 * -3 + c * -3) + 10(c + -5) 3 + -6c = (-12 + -3c) + 10(c + -5) Reorder the terms: 3 + -6c = -12 + -3c + 10(-5 + c) 3 + -6c = -12 + -3c + (-5 * 10 + c * 10) 3 + -6c = -12 + -3c + (-50 + 10c) Reorder the terms: 3 + -6c = -12 + -50 + -3c + 10c Combine like terms: -12 + -50 = -62 3 + -6c = -62 + -3c + 10c Combine like terms: -3c + 10c = 7c 3 + -6c = -62 + 7c Solving 3 + -6c = -62 + 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. 3 + -6c + -7c = -62 + 7c + -7c Combine like terms: -6c + -7c = -13c 3 + -13c = -62 + 7c + -7c Combine like terms: 7c + -7c = 0 3 + -13c = -62 + 0 3 + -13c = -62 Add '-3' to each side of the equation. 3 + -3 + -13c = -62 + -3 Combine like terms: 3 + -3 = 0 0 + -13c = -62 + -3 -13c = -62 + -3 Combine like terms: -62 + -3 = -65 -13c = -65 Divide each side by '-13'. c = 5 Simplifying c = 5
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