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Simplifying 5(4x + -7) + 3(x + 2) = 6(x + 6) + -1(x + 4) Reorder the terms: 5(-7 + 4x) + 3(x + 2) = 6(x + 6) + -1(x + 4) (-7 * 5 + 4x * 5) + 3(x + 2) = 6(x + 6) + -1(x + 4) (-35 + 20x) + 3(x + 2) = 6(x + 6) + -1(x + 4) Reorder the terms: -35 + 20x + 3(2 + x) = 6(x + 6) + -1(x + 4) -35 + 20x + (2 * 3 + x * 3) = 6(x + 6) + -1(x + 4) -35 + 20x + (6 + 3x) = 6(x + 6) + -1(x + 4) Reorder the terms: -35 + 6 + 20x + 3x = 6(x + 6) + -1(x + 4) Combine like terms: -35 + 6 = -29 -29 + 20x + 3x = 6(x + 6) + -1(x + 4) Combine like terms: 20x + 3x = 23x -29 + 23x = 6(x + 6) + -1(x + 4) Reorder the terms: -29 + 23x = 6(6 + x) + -1(x + 4) -29 + 23x = (6 * 6 + x * 6) + -1(x + 4) -29 + 23x = (36 + 6x) + -1(x + 4) Reorder the terms: -29 + 23x = 36 + 6x + -1(4 + x) -29 + 23x = 36 + 6x + (4 * -1 + x * -1) -29 + 23x = 36 + 6x + (-4 + -1x) Reorder the terms: -29 + 23x = 36 + -4 + 6x + -1x Combine like terms: 36 + -4 = 32 -29 + 23x = 32 + 6x + -1x Combine like terms: 6x + -1x = 5x -29 + 23x = 32 + 5x Solving -29 + 23x = 32 + 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. -29 + 23x + -5x = 32 + 5x + -5x Combine like terms: 23x + -5x = 18x -29 + 18x = 32 + 5x + -5x Combine like terms: 5x + -5x = 0 -29 + 18x = 32 + 0 -29 + 18x = 32 Add '29' to each side of the equation. -29 + 29 + 18x = 32 + 29 Combine like terms: -29 + 29 = 0 0 + 18x = 32 + 29 18x = 32 + 29 Combine like terms: 32 + 29 = 61 18x = 61 Divide each side by '18'. x = 3.388888889 Simplifying x = 3.388888889
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