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Simplifying -6(x + 9) + -6(4x + 8) = -31(x + 3) + 4 Reorder the terms: -6(9 + x) + -6(4x + 8) = -31(x + 3) + 4 (9 * -6 + x * -6) + -6(4x + 8) = -31(x + 3) + 4 (-54 + -6x) + -6(4x + 8) = -31(x + 3) + 4 Reorder the terms: -54 + -6x + -6(8 + 4x) = -31(x + 3) + 4 -54 + -6x + (8 * -6 + 4x * -6) = -31(x + 3) + 4 -54 + -6x + (-48 + -24x) = -31(x + 3) + 4 Reorder the terms: -54 + -48 + -6x + -24x = -31(x + 3) + 4 Combine like terms: -54 + -48 = -102 -102 + -6x + -24x = -31(x + 3) + 4 Combine like terms: -6x + -24x = -30x -102 + -30x = -31(x + 3) + 4 Reorder the terms: -102 + -30x = -31(3 + x) + 4 -102 + -30x = (3 * -31 + x * -31) + 4 -102 + -30x = (-93 + -31x) + 4 Reorder the terms: -102 + -30x = -93 + 4 + -31x Combine like terms: -93 + 4 = -89 -102 + -30x = -89 + -31x Solving -102 + -30x = -89 + -31x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31x' to each side of the equation. -102 + -30x + 31x = -89 + -31x + 31x Combine like terms: -30x + 31x = 1x -102 + 1x = -89 + -31x + 31x Combine like terms: -31x + 31x = 0 -102 + 1x = -89 + 0 -102 + 1x = -89 Add '102' to each side of the equation. -102 + 102 + 1x = -89 + 102 Combine like terms: -102 + 102 = 0 0 + 1x = -89 + 102 1x = -89 + 102 Combine like terms: -89 + 102 = 13 1x = 13 Divide each side by '1'. x = 13 Simplifying x = 13
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