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Simplifying 6(x + -7) + -7(x + -6) = x + 6(x + -4) Reorder the terms: 6(-7 + x) + -7(x + -6) = x + 6(x + -4) (-7 * 6 + x * 6) + -7(x + -6) = x + 6(x + -4) (-42 + 6x) + -7(x + -6) = x + 6(x + -4) Reorder the terms: -42 + 6x + -7(-6 + x) = x + 6(x + -4) -42 + 6x + (-6 * -7 + x * -7) = x + 6(x + -4) -42 + 6x + (42 + -7x) = x + 6(x + -4) Reorder the terms: -42 + 42 + 6x + -7x = x + 6(x + -4) Combine like terms: -42 + 42 = 0 0 + 6x + -7x = x + 6(x + -4) 6x + -7x = x + 6(x + -4) Combine like terms: 6x + -7x = -1x -1x = x + 6(x + -4) Reorder the terms: -1x = x + 6(-4 + x) -1x = x + (-4 * 6 + x * 6) -1x = x + (-24 + 6x) Reorder the terms: -1x = -24 + x + 6x Combine like terms: x + 6x = 7x -1x = -24 + 7x Solving -1x = -24 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. -1x + -7x = -24 + 7x + -7x Combine like terms: -1x + -7x = -8x -8x = -24 + 7x + -7x Combine like terms: 7x + -7x = 0 -8x = -24 + 0 -8x = -24 Divide each side by '-8'. x = 3 Simplifying x = 3
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