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Simplifying 2(-5) + 7(5x + 6) + 4(5 + -7x) = 3(2x + -7) + -11 + 5(x + -8) Multiply 2 * -5 -10 + 7(5x + 6) + 4(5 + -7x) = 3(2x + -7) + -11 + 5(x + -8) Reorder the terms: -10 + 7(6 + 5x) + 4(5 + -7x) = 3(2x + -7) + -11 + 5(x + -8) -10 + (6 * 7 + 5x * 7) + 4(5 + -7x) = 3(2x + -7) + -11 + 5(x + -8) -10 + (42 + 35x) + 4(5 + -7x) = 3(2x + -7) + -11 + 5(x + -8) -10 + 42 + 35x + (5 * 4 + -7x * 4) = 3(2x + -7) + -11 + 5(x + -8) -10 + 42 + 35x + (20 + -28x) = 3(2x + -7) + -11 + 5(x + -8) Reorder the terms: -10 + 42 + 20 + 35x + -28x = 3(2x + -7) + -11 + 5(x + -8) Combine like terms: -10 + 42 = 32 32 + 20 + 35x + -28x = 3(2x + -7) + -11 + 5(x + -8) Combine like terms: 32 + 20 = 52 52 + 35x + -28x = 3(2x + -7) + -11 + 5(x + -8) Combine like terms: 35x + -28x = 7x 52 + 7x = 3(2x + -7) + -11 + 5(x + -8) Reorder the terms: 52 + 7x = 3(-7 + 2x) + -11 + 5(x + -8) 52 + 7x = (-7 * 3 + 2x * 3) + -11 + 5(x + -8) 52 + 7x = (-21 + 6x) + -11 + 5(x + -8) Reorder the terms: 52 + 7x = -21 + 6x + -11 + 5(-8 + x) 52 + 7x = -21 + 6x + -11 + (-8 * 5 + x * 5) 52 + 7x = -21 + 6x + -11 + (-40 + 5x) Reorder the terms: 52 + 7x = -21 + -11 + -40 + 6x + 5x Combine like terms: -21 + -11 = -32 52 + 7x = -32 + -40 + 6x + 5x Combine like terms: -32 + -40 = -72 52 + 7x = -72 + 6x + 5x Combine like terms: 6x + 5x = 11x 52 + 7x = -72 + 11x Solving 52 + 7x = -72 + 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. 52 + 7x + -11x = -72 + 11x + -11x Combine like terms: 7x + -11x = -4x 52 + -4x = -72 + 11x + -11x Combine like terms: 11x + -11x = 0 52 + -4x = -72 + 0 52 + -4x = -72 Add '-52' to each side of the equation. 52 + -52 + -4x = -72 + -52 Combine like terms: 52 + -52 = 0 0 + -4x = -72 + -52 -4x = -72 + -52 Combine like terms: -72 + -52 = -124 -4x = -124 Divide each side by '-4'. x = 31 Simplifying x = 31
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