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Simplifying 7(x + -3) + 2(x + -1) + -5(x + 4) = 8(3x + 1) + -8(3x + 1) + x + 19 Reorder the terms: 7(-3 + x) + 2(x + -1) + -5(x + 4) = 8(3x + 1) + -8(3x + 1) + x + 19 (-3 * 7 + x * 7) + 2(x + -1) + -5(x + 4) = 8(3x + 1) + -8(3x + 1) + x + 19 (-21 + 7x) + 2(x + -1) + -5(x + 4) = 8(3x + 1) + -8(3x + 1) + x + 19 Reorder the terms: -21 + 7x + 2(-1 + x) + -5(x + 4) = 8(3x + 1) + -8(3x + 1) + x + 19 -21 + 7x + (-1 * 2 + x * 2) + -5(x + 4) = 8(3x + 1) + -8(3x + 1) + x + 19 -21 + 7x + (-2 + 2x) + -5(x + 4) = 8(3x + 1) + -8(3x + 1) + x + 19 Reorder the terms: -21 + 7x + -2 + 2x + -5(4 + x) = 8(3x + 1) + -8(3x + 1) + x + 19 -21 + 7x + -2 + 2x + (4 * -5 + x * -5) = 8(3x + 1) + -8(3x + 1) + x + 19 -21 + 7x + -2 + 2x + (-20 + -5x) = 8(3x + 1) + -8(3x + 1) + x + 19 Reorder the terms: -21 + -2 + -20 + 7x + 2x + -5x = 8(3x + 1) + -8(3x + 1) + x + 19 Combine like terms: -21 + -2 = -23 -23 + -20 + 7x + 2x + -5x = 8(3x + 1) + -8(3x + 1) + x + 19 Combine like terms: -23 + -20 = -43 -43 + 7x + 2x + -5x = 8(3x + 1) + -8(3x + 1) + x + 19 Combine like terms: 7x + 2x = 9x -43 + 9x + -5x = 8(3x + 1) + -8(3x + 1) + x + 19 Combine like terms: 9x + -5x = 4x -43 + 4x = 8(3x + 1) + -8(3x + 1) + x + 19 Reorder the terms: -43 + 4x = 8(1 + 3x) + -8(3x + 1) + x + 19 -43 + 4x = (1 * 8 + 3x * 8) + -8(3x + 1) + x + 19 -43 + 4x = (8 + 24x) + -8(3x + 1) + x + 19 Reorder the terms: -43 + 4x = 8 + 24x + -8(1 + 3x) + x + 19 -43 + 4x = 8 + 24x + (1 * -8 + 3x * -8) + x + 19 -43 + 4x = 8 + 24x + (-8 + -24x) + x + 19 Reorder the terms: -43 + 4x = 8 + -8 + 19 + 24x + -24x + x Combine like terms: 8 + -8 = 0 -43 + 4x = 0 + 19 + 24x + -24x + x -43 + 4x = 19 + 24x + -24x + x Combine like terms: 24x + -24x = 0 -43 + 4x = 19 + 0 + x -43 + 4x = 19 + x Solving -43 + 4x = 19 + x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. -43 + 4x + -1x = 19 + x + -1x Combine like terms: 4x + -1x = 3x -43 + 3x = 19 + x + -1x Combine like terms: x + -1x = 0 -43 + 3x = 19 + 0 -43 + 3x = 19 Add '43' to each side of the equation. -43 + 43 + 3x = 19 + 43 Combine like terms: -43 + 43 = 0 0 + 3x = 19 + 43 3x = 19 + 43 Combine like terms: 19 + 43 = 62 3x = 62 Divide each side by '3'. x = 20.66666667 Simplifying x = 20.66666667
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