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Simplifying 2(3x + 2) + -4(2x + 3) = 3(2x + -1) + -6(x + -5) Reorder the terms: 2(2 + 3x) + -4(2x + 3) = 3(2x + -1) + -6(x + -5) (2 * 2 + 3x * 2) + -4(2x + 3) = 3(2x + -1) + -6(x + -5) (4 + 6x) + -4(2x + 3) = 3(2x + -1) + -6(x + -5) Reorder the terms: 4 + 6x + -4(3 + 2x) = 3(2x + -1) + -6(x + -5) 4 + 6x + (3 * -4 + 2x * -4) = 3(2x + -1) + -6(x + -5) 4 + 6x + (-12 + -8x) = 3(2x + -1) + -6(x + -5) Reorder the terms: 4 + -12 + 6x + -8x = 3(2x + -1) + -6(x + -5) Combine like terms: 4 + -12 = -8 -8 + 6x + -8x = 3(2x + -1) + -6(x + -5) Combine like terms: 6x + -8x = -2x -8 + -2x = 3(2x + -1) + -6(x + -5) Reorder the terms: -8 + -2x = 3(-1 + 2x) + -6(x + -5) -8 + -2x = (-1 * 3 + 2x * 3) + -6(x + -5) -8 + -2x = (-3 + 6x) + -6(x + -5) Reorder the terms: -8 + -2x = -3 + 6x + -6(-5 + x) -8 + -2x = -3 + 6x + (-5 * -6 + x * -6) -8 + -2x = -3 + 6x + (30 + -6x) Reorder the terms: -8 + -2x = -3 + 30 + 6x + -6x Combine like terms: -3 + 30 = 27 -8 + -2x = 27 + 6x + -6x Combine like terms: 6x + -6x = 0 -8 + -2x = 27 + 0 -8 + -2x = 27 Solving -8 + -2x = 27 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -2x = 27 + 8 Combine like terms: -8 + 8 = 0 0 + -2x = 27 + 8 -2x = 27 + 8 Combine like terms: 27 + 8 = 35 -2x = 35 Divide each side by '-2'. x = -17.5 Simplifying x = -17.5
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