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Simplifying 4(x + 4) + 7(x + 3) = 8(3x + 1) + 6(x + -4) Reorder the terms: 4(4 + x) + 7(x + 3) = 8(3x + 1) + 6(x + -4) (4 * 4 + x * 4) + 7(x + 3) = 8(3x + 1) + 6(x + -4) (16 + 4x) + 7(x + 3) = 8(3x + 1) + 6(x + -4) Reorder the terms: 16 + 4x + 7(3 + x) = 8(3x + 1) + 6(x + -4) 16 + 4x + (3 * 7 + x * 7) = 8(3x + 1) + 6(x + -4) 16 + 4x + (21 + 7x) = 8(3x + 1) + 6(x + -4) Reorder the terms: 16 + 21 + 4x + 7x = 8(3x + 1) + 6(x + -4) Combine like terms: 16 + 21 = 37 37 + 4x + 7x = 8(3x + 1) + 6(x + -4) Combine like terms: 4x + 7x = 11x 37 + 11x = 8(3x + 1) + 6(x + -4) Reorder the terms: 37 + 11x = 8(1 + 3x) + 6(x + -4) 37 + 11x = (1 * 8 + 3x * 8) + 6(x + -4) 37 + 11x = (8 + 24x) + 6(x + -4) Reorder the terms: 37 + 11x = 8 + 24x + 6(-4 + x) 37 + 11x = 8 + 24x + (-4 * 6 + x * 6) 37 + 11x = 8 + 24x + (-24 + 6x) Reorder the terms: 37 + 11x = 8 + -24 + 24x + 6x Combine like terms: 8 + -24 = -16 37 + 11x = -16 + 24x + 6x Combine like terms: 24x + 6x = 30x 37 + 11x = -16 + 30x Solving 37 + 11x = -16 + 30x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30x' to each side of the equation. 37 + 11x + -30x = -16 + 30x + -30x Combine like terms: 11x + -30x = -19x 37 + -19x = -16 + 30x + -30x Combine like terms: 30x + -30x = 0 37 + -19x = -16 + 0 37 + -19x = -16 Add '-37' to each side of the equation. 37 + -37 + -19x = -16 + -37 Combine like terms: 37 + -37 = 0 0 + -19x = -16 + -37 -19x = -16 + -37 Combine like terms: -16 + -37 = -53 -19x = -53 Divide each side by '-19'. x = 2.789473684 Simplifying x = 2.789473684
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