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Simplifying 24(x + 13) + 23(x + 14) = 32(10 + -1x) Reorder the terms: 24(13 + x) + 23(x + 14) = 32(10 + -1x) (13 * 24 + x * 24) + 23(x + 14) = 32(10 + -1x) (312 + 24x) + 23(x + 14) = 32(10 + -1x) Reorder the terms: 312 + 24x + 23(14 + x) = 32(10 + -1x) 312 + 24x + (14 * 23 + x * 23) = 32(10 + -1x) 312 + 24x + (322 + 23x) = 32(10 + -1x) Reorder the terms: 312 + 322 + 24x + 23x = 32(10 + -1x) Combine like terms: 312 + 322 = 634 634 + 24x + 23x = 32(10 + -1x) Combine like terms: 24x + 23x = 47x 634 + 47x = 32(10 + -1x) 634 + 47x = (10 * 32 + -1x * 32) 634 + 47x = (320 + -32x) Solving 634 + 47x = 320 + -32x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32x' to each side of the equation. 634 + 47x + 32x = 320 + -32x + 32x Combine like terms: 47x + 32x = 79x 634 + 79x = 320 + -32x + 32x Combine like terms: -32x + 32x = 0 634 + 79x = 320 + 0 634 + 79x = 320 Add '-634' to each side of the equation. 634 + -634 + 79x = 320 + -634 Combine like terms: 634 + -634 = 0 0 + 79x = 320 + -634 79x = 320 + -634 Combine like terms: 320 + -634 = -314 79x = -314 Divide each side by '79'. x = -3.974683544 Simplifying x = -3.974683544
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