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Simplifying 6(c + 0.5) + 7(2c + -1) = 32 + -4(3c + -7) Reorder the terms: 6(0.5 + c) + 7(2c + -1) = 32 + -4(3c + -7) (0.5 * 6 + c * 6) + 7(2c + -1) = 32 + -4(3c + -7) (3 + 6c) + 7(2c + -1) = 32 + -4(3c + -7) Reorder the terms: 3 + 6c + 7(-1 + 2c) = 32 + -4(3c + -7) 3 + 6c + (-1 * 7 + 2c * 7) = 32 + -4(3c + -7) 3 + 6c + (-7 + 14c) = 32 + -4(3c + -7) Reorder the terms: 3 + -7 + 6c + 14c = 32 + -4(3c + -7) Combine like terms: 3 + -7 = -4 -4 + 6c + 14c = 32 + -4(3c + -7) Combine like terms: 6c + 14c = 20c -4 + 20c = 32 + -4(3c + -7) Reorder the terms: -4 + 20c = 32 + -4(-7 + 3c) -4 + 20c = 32 + (-7 * -4 + 3c * -4) -4 + 20c = 32 + (28 + -12c) Combine like terms: 32 + 28 = 60 -4 + 20c = 60 + -12c Solving -4 + 20c = 60 + -12c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '12c' to each side of the equation. -4 + 20c + 12c = 60 + -12c + 12c Combine like terms: 20c + 12c = 32c -4 + 32c = 60 + -12c + 12c Combine like terms: -12c + 12c = 0 -4 + 32c = 60 + 0 -4 + 32c = 60 Add '4' to each side of the equation. -4 + 4 + 32c = 60 + 4 Combine like terms: -4 + 4 = 0 0 + 32c = 60 + 4 32c = 60 + 4 Combine like terms: 60 + 4 = 64 32c = 64 Divide each side by '32'. c = 2 Simplifying c = 2
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