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Simplifying (0.5x + 4)(2x + 6 + -17) = 39 + -1(x + -1)(8 + -1x) Reorder the terms: (4 + 0.5x)(2x + 6 + -17) = 39 + -1(x + -1)(8 + -1x) Reorder the terms: (4 + 0.5x)(6 + -17 + 2x) = 39 + -1(x + -1)(8 + -1x) Combine like terms: 6 + -17 = -11 (4 + 0.5x)(-11 + 2x) = 39 + -1(x + -1)(8 + -1x) Multiply (4 + 0.5x) * (-11 + 2x) (4(-11 + 2x) + 0.5x * (-11 + 2x)) = 39 + -1(x + -1)(8 + -1x) ((-11 * 4 + 2x * 4) + 0.5x * (-11 + 2x)) = 39 + -1(x + -1)(8 + -1x) ((-44 + 8x) + 0.5x * (-11 + 2x)) = 39 + -1(x + -1)(8 + -1x) (-44 + 8x + (-11 * 0.5x + 2x * 0.5x)) = 39 + -1(x + -1)(8 + -1x) (-44 + 8x + (-5.5x + 1x2)) = 39 + -1(x + -1)(8 + -1x) Combine like terms: 8x + -5.5x = 2.5x (-44 + 2.5x + 1x2) = 39 + -1(x + -1)(8 + -1x) Reorder the terms: -44 + 2.5x + 1x2 = 39 + -1(-1 + x)(8 + -1x) Multiply (-1 + x) * (8 + -1x) -44 + 2.5x + 1x2 = 39 + -1(-1(8 + -1x) + x(8 + -1x)) -44 + 2.5x + 1x2 = 39 + -1((8 * -1 + -1x * -1) + x(8 + -1x)) -44 + 2.5x + 1x2 = 39 + -1((-8 + 1x) + x(8 + -1x)) -44 + 2.5x + 1x2 = 39 + -1(-8 + 1x + (8 * x + -1x * x)) -44 + 2.5x + 1x2 = 39 + -1(-8 + 1x + (8x + -1x2)) Combine like terms: 1x + 8x = 9x -44 + 2.5x + 1x2 = 39 + -1(-8 + 9x + -1x2) -44 + 2.5x + 1x2 = 39 + (-8 * -1 + 9x * -1 + -1x2 * -1) -44 + 2.5x + 1x2 = 39 + (8 + -9x + 1x2) Combine like terms: 39 + 8 = 47 -44 + 2.5x + 1x2 = 47 + -9x + 1x2 Add '-1x2' to each side of the equation. -44 + 2.5x + 1x2 + -1x2 = 47 + -9x + 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -44 + 2.5x + 0 = 47 + -9x + 1x2 + -1x2 -44 + 2.5x = 47 + -9x + 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -44 + 2.5x = 47 + -9x + 0 -44 + 2.5x = 47 + -9x Solving -44 + 2.5x = 47 + -9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9x' to each side of the equation. -44 + 2.5x + 9x = 47 + -9x + 9x Combine like terms: 2.5x + 9x = 11.5x -44 + 11.5x = 47 + -9x + 9x Combine like terms: -9x + 9x = 0 -44 + 11.5x = 47 + 0 -44 + 11.5x = 47 Add '44' to each side of the equation. -44 + 44 + 11.5x = 47 + 44 Combine like terms: -44 + 44 = 0 0 + 11.5x = 47 + 44 11.5x = 47 + 44 Combine like terms: 47 + 44 = 91 11.5x = 91 Divide each side by '11.5'. x = 7.913043478 Simplifying x = 7.913043478
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