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Simplifying 24(3x + -1) + -20(5x + 1) = 15(x + 1) + -3 * 120 Reorder the terms: 24(-1 + 3x) + -20(5x + 1) = 15(x + 1) + -3 * 120 (-1 * 24 + 3x * 24) + -20(5x + 1) = 15(x + 1) + -3 * 120 (-24 + 72x) + -20(5x + 1) = 15(x + 1) + -3 * 120 Reorder the terms: -24 + 72x + -20(1 + 5x) = 15(x + 1) + -3 * 120 -24 + 72x + (1 * -20 + 5x * -20) = 15(x + 1) + -3 * 120 -24 + 72x + (-20 + -100x) = 15(x + 1) + -3 * 120 Reorder the terms: -24 + -20 + 72x + -100x = 15(x + 1) + -3 * 120 Combine like terms: -24 + -20 = -44 -44 + 72x + -100x = 15(x + 1) + -3 * 120 Combine like terms: 72x + -100x = -28x -44 + -28x = 15(x + 1) + -3 * 120 Reorder the terms: -44 + -28x = 15(1 + x) + -3 * 120 -44 + -28x = (1 * 15 + x * 15) + -3 * 120 -44 + -28x = (15 + 15x) + -3 * 120 Multiply -3 * 120 -44 + -28x = 15 + 15x + -360 Reorder the terms: -44 + -28x = 15 + -360 + 15x Combine like terms: 15 + -360 = -345 -44 + -28x = -345 + 15x Solving -44 + -28x = -345 + 15x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15x' to each side of the equation. -44 + -28x + -15x = -345 + 15x + -15x Combine like terms: -28x + -15x = -43x -44 + -43x = -345 + 15x + -15x Combine like terms: 15x + -15x = 0 -44 + -43x = -345 + 0 -44 + -43x = -345 Add '44' to each side of the equation. -44 + 44 + -43x = -345 + 44 Combine like terms: -44 + 44 = 0 0 + -43x = -345 + 44 -43x = -345 + 44 Combine like terms: -345 + 44 = -301 -43x = -301 Divide each side by '-43'. x = 7 Simplifying x = 7
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