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Simplifying 3(-5 + c) + -2(c + -4) = 2 + -7(c + -1) (-5 * 3 + c * 3) + -2(c + -4) = 2 + -7(c + -1) (-15 + 3c) + -2(c + -4) = 2 + -7(c + -1) Reorder the terms: -15 + 3c + -2(-4 + c) = 2 + -7(c + -1) -15 + 3c + (-4 * -2 + c * -2) = 2 + -7(c + -1) -15 + 3c + (8 + -2c) = 2 + -7(c + -1) Reorder the terms: -15 + 8 + 3c + -2c = 2 + -7(c + -1) Combine like terms: -15 + 8 = -7 -7 + 3c + -2c = 2 + -7(c + -1) Combine like terms: 3c + -2c = 1c -7 + 1c = 2 + -7(c + -1) Reorder the terms: -7 + 1c = 2 + -7(-1 + c) -7 + 1c = 2 + (-1 * -7 + c * -7) -7 + 1c = 2 + (7 + -7c) Combine like terms: 2 + 7 = 9 -7 + 1c = 9 + -7c Solving -7 + 1c = 9 + -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. -7 + 1c + 7c = 9 + -7c + 7c Combine like terms: 1c + 7c = 8c -7 + 8c = 9 + -7c + 7c Combine like terms: -7c + 7c = 0 -7 + 8c = 9 + 0 -7 + 8c = 9 Add '7' to each side of the equation. -7 + 7 + 8c = 9 + 7 Combine like terms: -7 + 7 = 0 0 + 8c = 9 + 7 8c = 9 + 7 Combine like terms: 9 + 7 = 16 8c = 16 Divide each side by '8'. c = 2 Simplifying c = 2
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