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Simplifying 4(2x + -3) + 6(4x + -11) + 7(6x + 21) = 1000 Reorder the terms: 4(-3 + 2x) + 6(4x + -11) + 7(6x + 21) = 1000 (-3 * 4 + 2x * 4) + 6(4x + -11) + 7(6x + 21) = 1000 (-12 + 8x) + 6(4x + -11) + 7(6x + 21) = 1000 Reorder the terms: -12 + 8x + 6(-11 + 4x) + 7(6x + 21) = 1000 -12 + 8x + (-11 * 6 + 4x * 6) + 7(6x + 21) = 1000 -12 + 8x + (-66 + 24x) + 7(6x + 21) = 1000 Reorder the terms: -12 + 8x + -66 + 24x + 7(21 + 6x) = 1000 -12 + 8x + -66 + 24x + (21 * 7 + 6x * 7) = 1000 -12 + 8x + -66 + 24x + (147 + 42x) = 1000 Reorder the terms: -12 + -66 + 147 + 8x + 24x + 42x = 1000 Combine like terms: -12 + -66 = -78 -78 + 147 + 8x + 24x + 42x = 1000 Combine like terms: -78 + 147 = 69 69 + 8x + 24x + 42x = 1000 Combine like terms: 8x + 24x = 32x 69 + 32x + 42x = 1000 Combine like terms: 32x + 42x = 74x 69 + 74x = 1000 Solving 69 + 74x = 1000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-69' to each side of the equation. 69 + -69 + 74x = 1000 + -69 Combine like terms: 69 + -69 = 0 0 + 74x = 1000 + -69 74x = 1000 + -69 Combine like terms: 1000 + -69 = 931 74x = 931 Divide each side by '74'. x = 12.58108108 Simplifying x = 12.58108108
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