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Simplifying -6(x + -21) + 7(x + 6) = 42(x + -5) Reorder the terms: -6(-21 + x) + 7(x + 6) = 42(x + -5) (-21 * -6 + x * -6) + 7(x + 6) = 42(x + -5) (126 + -6x) + 7(x + 6) = 42(x + -5) Reorder the terms: 126 + -6x + 7(6 + x) = 42(x + -5) 126 + -6x + (6 * 7 + x * 7) = 42(x + -5) 126 + -6x + (42 + 7x) = 42(x + -5) Reorder the terms: 126 + 42 + -6x + 7x = 42(x + -5) Combine like terms: 126 + 42 = 168 168 + -6x + 7x = 42(x + -5) Combine like terms: -6x + 7x = 1x 168 + 1x = 42(x + -5) Reorder the terms: 168 + 1x = 42(-5 + x) 168 + 1x = (-5 * 42 + x * 42) 168 + 1x = (-210 + 42x) Solving 168 + 1x = -210 + 42x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42x' to each side of the equation. 168 + 1x + -42x = -210 + 42x + -42x Combine like terms: 1x + -42x = -41x 168 + -41x = -210 + 42x + -42x Combine like terms: 42x + -42x = 0 168 + -41x = -210 + 0 168 + -41x = -210 Add '-168' to each side of the equation. 168 + -168 + -41x = -210 + -168 Combine like terms: 168 + -168 = 0 0 + -41x = -210 + -168 -41x = -210 + -168 Combine like terms: -210 + -168 = -378 -41x = -378 Divide each side by '-41'. x = 9.219512195 Simplifying x = 9.219512195
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