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Simplifying 8(6x + 1) + -1(8 + -4x) + 4(2x + 10) = 30 + 15(2x + -10) + -40(1 + -5x) Reorder the terms: 8(1 + 6x) + -1(8 + -4x) + 4(2x + 10) = 30 + 15(2x + -10) + -40(1 + -5x) (1 * 8 + 6x * 8) + -1(8 + -4x) + 4(2x + 10) = 30 + 15(2x + -10) + -40(1 + -5x) (8 + 48x) + -1(8 + -4x) + 4(2x + 10) = 30 + 15(2x + -10) + -40(1 + -5x) 8 + 48x + (8 * -1 + -4x * -1) + 4(2x + 10) = 30 + 15(2x + -10) + -40(1 + -5x) 8 + 48x + (-8 + 4x) + 4(2x + 10) = 30 + 15(2x + -10) + -40(1 + -5x) Reorder the terms: 8 + 48x + -8 + 4x + 4(10 + 2x) = 30 + 15(2x + -10) + -40(1 + -5x) 8 + 48x + -8 + 4x + (10 * 4 + 2x * 4) = 30 + 15(2x + -10) + -40(1 + -5x) 8 + 48x + -8 + 4x + (40 + 8x) = 30 + 15(2x + -10) + -40(1 + -5x) Reorder the terms: 8 + -8 + 40 + 48x + 4x + 8x = 30 + 15(2x + -10) + -40(1 + -5x) Combine like terms: 8 + -8 = 0 0 + 40 + 48x + 4x + 8x = 30 + 15(2x + -10) + -40(1 + -5x) 40 + 48x + 4x + 8x = 30 + 15(2x + -10) + -40(1 + -5x) Combine like terms: 48x + 4x = 52x 40 + 52x + 8x = 30 + 15(2x + -10) + -40(1 + -5x) Combine like terms: 52x + 8x = 60x 40 + 60x = 30 + 15(2x + -10) + -40(1 + -5x) Reorder the terms: 40 + 60x = 30 + 15(-10 + 2x) + -40(1 + -5x) 40 + 60x = 30 + (-10 * 15 + 2x * 15) + -40(1 + -5x) 40 + 60x = 30 + (-150 + 30x) + -40(1 + -5x) 40 + 60x = 30 + -150 + 30x + (1 * -40 + -5x * -40) 40 + 60x = 30 + -150 + 30x + (-40 + 200x) Reorder the terms: 40 + 60x = 30 + -150 + -40 + 30x + 200x Combine like terms: 30 + -150 = -120 40 + 60x = -120 + -40 + 30x + 200x Combine like terms: -120 + -40 = -160 40 + 60x = -160 + 30x + 200x Combine like terms: 30x + 200x = 230x 40 + 60x = -160 + 230x Solving 40 + 60x = -160 + 230x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-230x' to each side of the equation. 40 + 60x + -230x = -160 + 230x + -230x Combine like terms: 60x + -230x = -170x 40 + -170x = -160 + 230x + -230x Combine like terms: 230x + -230x = 0 40 + -170x = -160 + 0 40 + -170x = -160 Add '-40' to each side of the equation. 40 + -40 + -170x = -160 + -40 Combine like terms: 40 + -40 = 0 0 + -170x = -160 + -40 -170x = -160 + -40 Combine like terms: -160 + -40 = -200 -170x = -200 Divide each side by '-170'. x = 1.176470588 Simplifying x = 1.176470588
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