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Simplifying 5(x + -2) + -3(1 + -1x) = 4(x + -3) + 31 Reorder the terms: 5(-2 + x) + -3(1 + -1x) = 4(x + -3) + 31 (-2 * 5 + x * 5) + -3(1 + -1x) = 4(x + -3) + 31 (-10 + 5x) + -3(1 + -1x) = 4(x + -3) + 31 -10 + 5x + (1 * -3 + -1x * -3) = 4(x + -3) + 31 -10 + 5x + (-3 + 3x) = 4(x + -3) + 31 Reorder the terms: -10 + -3 + 5x + 3x = 4(x + -3) + 31 Combine like terms: -10 + -3 = -13 -13 + 5x + 3x = 4(x + -3) + 31 Combine like terms: 5x + 3x = 8x -13 + 8x = 4(x + -3) + 31 Reorder the terms: -13 + 8x = 4(-3 + x) + 31 -13 + 8x = (-3 * 4 + x * 4) + 31 -13 + 8x = (-12 + 4x) + 31 Reorder the terms: -13 + 8x = -12 + 31 + 4x Combine like terms: -12 + 31 = 19 -13 + 8x = 19 + 4x Solving -13 + 8x = 19 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. -13 + 8x + -4x = 19 + 4x + -4x Combine like terms: 8x + -4x = 4x -13 + 4x = 19 + 4x + -4x Combine like terms: 4x + -4x = 0 -13 + 4x = 19 + 0 -13 + 4x = 19 Add '13' to each side of the equation. -13 + 13 + 4x = 19 + 13 Combine like terms: -13 + 13 = 0 0 + 4x = 19 + 13 4x = 19 + 13 Combine like terms: 19 + 13 = 32 4x = 32 Divide each side by '4'. x = 8 Simplifying x = 8
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