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Simplifying 3(2x + -5) + -2(5x + 4) = 7(2x + -1) + -1(3x + 1) Reorder the terms: 3(-5 + 2x) + -2(5x + 4) = 7(2x + -1) + -1(3x + 1) (-5 * 3 + 2x * 3) + -2(5x + 4) = 7(2x + -1) + -1(3x + 1) (-15 + 6x) + -2(5x + 4) = 7(2x + -1) + -1(3x + 1) Reorder the terms: -15 + 6x + -2(4 + 5x) = 7(2x + -1) + -1(3x + 1) -15 + 6x + (4 * -2 + 5x * -2) = 7(2x + -1) + -1(3x + 1) -15 + 6x + (-8 + -10x) = 7(2x + -1) + -1(3x + 1) Reorder the terms: -15 + -8 + 6x + -10x = 7(2x + -1) + -1(3x + 1) Combine like terms: -15 + -8 = -23 -23 + 6x + -10x = 7(2x + -1) + -1(3x + 1) Combine like terms: 6x + -10x = -4x -23 + -4x = 7(2x + -1) + -1(3x + 1) Reorder the terms: -23 + -4x = 7(-1 + 2x) + -1(3x + 1) -23 + -4x = (-1 * 7 + 2x * 7) + -1(3x + 1) -23 + -4x = (-7 + 14x) + -1(3x + 1) Reorder the terms: -23 + -4x = -7 + 14x + -1(1 + 3x) -23 + -4x = -7 + 14x + (1 * -1 + 3x * -1) -23 + -4x = -7 + 14x + (-1 + -3x) Reorder the terms: -23 + -4x = -7 + -1 + 14x + -3x Combine like terms: -7 + -1 = -8 -23 + -4x = -8 + 14x + -3x Combine like terms: 14x + -3x = 11x -23 + -4x = -8 + 11x Solving -23 + -4x = -8 + 11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11x' to each side of the equation. -23 + -4x + -11x = -8 + 11x + -11x Combine like terms: -4x + -11x = -15x -23 + -15x = -8 + 11x + -11x Combine like terms: 11x + -11x = 0 -23 + -15x = -8 + 0 -23 + -15x = -8 Add '23' to each side of the equation. -23 + 23 + -15x = -8 + 23 Combine like terms: -23 + 23 = 0 0 + -15x = -8 + 23 -15x = -8 + 23 Combine like terms: -8 + 23 = 15 -15x = 15 Divide each side by '-15'. x = -1 Simplifying x = -1
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