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Simplifying 12(2x + 1) + -15(x + 3) = 5(1 + -1x) + 32 Reorder the terms: 12(1 + 2x) + -15(x + 3) = 5(1 + -1x) + 32 (1 * 12 + 2x * 12) + -15(x + 3) = 5(1 + -1x) + 32 (12 + 24x) + -15(x + 3) = 5(1 + -1x) + 32 Reorder the terms: 12 + 24x + -15(3 + x) = 5(1 + -1x) + 32 12 + 24x + (3 * -15 + x * -15) = 5(1 + -1x) + 32 12 + 24x + (-45 + -15x) = 5(1 + -1x) + 32 Reorder the terms: 12 + -45 + 24x + -15x = 5(1 + -1x) + 32 Combine like terms: 12 + -45 = -33 -33 + 24x + -15x = 5(1 + -1x) + 32 Combine like terms: 24x + -15x = 9x -33 + 9x = 5(1 + -1x) + 32 -33 + 9x = (1 * 5 + -1x * 5) + 32 -33 + 9x = (5 + -5x) + 32 Reorder the terms: -33 + 9x = 5 + 32 + -5x Combine like terms: 5 + 32 = 37 -33 + 9x = 37 + -5x Solving -33 + 9x = 37 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. -33 + 9x + 5x = 37 + -5x + 5x Combine like terms: 9x + 5x = 14x -33 + 14x = 37 + -5x + 5x Combine like terms: -5x + 5x = 0 -33 + 14x = 37 + 0 -33 + 14x = 37 Add '33' to each side of the equation. -33 + 33 + 14x = 37 + 33 Combine like terms: -33 + 33 = 0 0 + 14x = 37 + 33 14x = 37 + 33 Combine like terms: 37 + 33 = 70 14x = 70 Divide each side by '14'. x = 5 Simplifying x = 5
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