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Simplifying 8(x + 8) + -5(9 + -5x) = 32(x + 1) + 10 Reorder the terms: 8(8 + x) + -5(9 + -5x) = 32(x + 1) + 10 (8 * 8 + x * 8) + -5(9 + -5x) = 32(x + 1) + 10 (64 + 8x) + -5(9 + -5x) = 32(x + 1) + 10 64 + 8x + (9 * -5 + -5x * -5) = 32(x + 1) + 10 64 + 8x + (-45 + 25x) = 32(x + 1) + 10 Reorder the terms: 64 + -45 + 8x + 25x = 32(x + 1) + 10 Combine like terms: 64 + -45 = 19 19 + 8x + 25x = 32(x + 1) + 10 Combine like terms: 8x + 25x = 33x 19 + 33x = 32(x + 1) + 10 Reorder the terms: 19 + 33x = 32(1 + x) + 10 19 + 33x = (1 * 32 + x * 32) + 10 19 + 33x = (32 + 32x) + 10 Reorder the terms: 19 + 33x = 32 + 10 + 32x Combine like terms: 32 + 10 = 42 19 + 33x = 42 + 32x Solving 19 + 33x = 42 + 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. 19 + 33x + -32x = 42 + 32x + -32x Combine like terms: 33x + -32x = 1x 19 + 1x = 42 + 32x + -32x Combine like terms: 32x + -32x = 0 19 + 1x = 42 + 0 19 + 1x = 42 Add '-19' to each side of the equation. 19 + -19 + 1x = 42 + -19 Combine like terms: 19 + -19 = 0 0 + 1x = 42 + -19 1x = 42 + -19 Combine like terms: 42 + -19 = 23 1x = 23 Divide each side by '1'. x = 23 Simplifying x = 23
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