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Simplifying 4(3x + -5) + -2(7 + -3x) = 6(2x + -3) + -5(2 + -3x) Reorder the terms: 4(-5 + 3x) + -2(7 + -3x) = 6(2x + -3) + -5(2 + -3x) (-5 * 4 + 3x * 4) + -2(7 + -3x) = 6(2x + -3) + -5(2 + -3x) (-20 + 12x) + -2(7 + -3x) = 6(2x + -3) + -5(2 + -3x) -20 + 12x + (7 * -2 + -3x * -2) = 6(2x + -3) + -5(2 + -3x) -20 + 12x + (-14 + 6x) = 6(2x + -3) + -5(2 + -3x) Reorder the terms: -20 + -14 + 12x + 6x = 6(2x + -3) + -5(2 + -3x) Combine like terms: -20 + -14 = -34 -34 + 12x + 6x = 6(2x + -3) + -5(2 + -3x) Combine like terms: 12x + 6x = 18x -34 + 18x = 6(2x + -3) + -5(2 + -3x) Reorder the terms: -34 + 18x = 6(-3 + 2x) + -5(2 + -3x) -34 + 18x = (-3 * 6 + 2x * 6) + -5(2 + -3x) -34 + 18x = (-18 + 12x) + -5(2 + -3x) -34 + 18x = -18 + 12x + (2 * -5 + -3x * -5) -34 + 18x = -18 + 12x + (-10 + 15x) Reorder the terms: -34 + 18x = -18 + -10 + 12x + 15x Combine like terms: -18 + -10 = -28 -34 + 18x = -28 + 12x + 15x Combine like terms: 12x + 15x = 27x -34 + 18x = -28 + 27x Solving -34 + 18x = -28 + 27x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27x' to each side of the equation. -34 + 18x + -27x = -28 + 27x + -27x Combine like terms: 18x + -27x = -9x -34 + -9x = -28 + 27x + -27x Combine like terms: 27x + -27x = 0 -34 + -9x = -28 + 0 -34 + -9x = -28 Add '34' to each side of the equation. -34 + 34 + -9x = -28 + 34 Combine like terms: -34 + 34 = 0 0 + -9x = -28 + 34 -9x = -28 + 34 Combine like terms: -28 + 34 = 6 -9x = 6 Divide each side by '-9'. x = -0.6666666667 Simplifying x = -0.6666666667
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