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Simplifying -5(1 + -2x) + 4(3 + -1x) = 7(3 + x) (1 * -5 + -2x * -5) + 4(3 + -1x) = 7(3 + x) (-5 + 10x) + 4(3 + -1x) = 7(3 + x) -5 + 10x + (3 * 4 + -1x * 4) = 7(3 + x) -5 + 10x + (12 + -4x) = 7(3 + x) Reorder the terms: -5 + 12 + 10x + -4x = 7(3 + x) Combine like terms: -5 + 12 = 7 7 + 10x + -4x = 7(3 + x) Combine like terms: 10x + -4x = 6x 7 + 6x = 7(3 + x) 7 + 6x = (3 * 7 + x * 7) 7 + 6x = (21 + 7x) Solving 7 + 6x = 21 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 7 + 6x + -7x = 21 + 7x + -7x Combine like terms: 6x + -7x = -1x 7 + -1x = 21 + 7x + -7x Combine like terms: 7x + -7x = 0 7 + -1x = 21 + 0 7 + -1x = 21 Add '-7' to each side of the equation. 7 + -7 + -1x = 21 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 21 + -7 -1x = 21 + -7 Combine like terms: 21 + -7 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14
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