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Simplifying 7(6x + -7) + 4(3x + -5) = 1(5x + 78) Reorder the terms: 7(-7 + 6x) + 4(3x + -5) = 1(5x + 78) (-7 * 7 + 6x * 7) + 4(3x + -5) = 1(5x + 78) (-49 + 42x) + 4(3x + -5) = 1(5x + 78) Reorder the terms: -49 + 42x + 4(-5 + 3x) = 1(5x + 78) -49 + 42x + (-5 * 4 + 3x * 4) = 1(5x + 78) -49 + 42x + (-20 + 12x) = 1(5x + 78) Reorder the terms: -49 + -20 + 42x + 12x = 1(5x + 78) Combine like terms: -49 + -20 = -69 -69 + 42x + 12x = 1(5x + 78) Combine like terms: 42x + 12x = 54x -69 + 54x = 1(5x + 78) Reorder the terms: -69 + 54x = 1(78 + 5x) -69 + 54x = (78 * 1 + 5x * 1) -69 + 54x = (78 + 5x) Solving -69 + 54x = 78 + 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. -69 + 54x + -5x = 78 + 5x + -5x Combine like terms: 54x + -5x = 49x -69 + 49x = 78 + 5x + -5x Combine like terms: 5x + -5x = 0 -69 + 49x = 78 + 0 -69 + 49x = 78 Add '69' to each side of the equation. -69 + 69 + 49x = 78 + 69 Combine like terms: -69 + 69 = 0 0 + 49x = 78 + 69 49x = 78 + 69 Combine like terms: 78 + 69 = 147 49x = 147 Divide each side by '49'. x = 3 Simplifying x = 3
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