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Simplifying 3(L + -7) + 2(2L + 5) = 5(L + -7) + 32 Reorder the terms: 3(-7 + L) + 2(2L + 5) = 5(L + -7) + 32 (-7 * 3 + L * 3) + 2(2L + 5) = 5(L + -7) + 32 (-21 + 3L) + 2(2L + 5) = 5(L + -7) + 32 Reorder the terms: -21 + 3L + 2(5 + 2L) = 5(L + -7) + 32 -21 + 3L + (5 * 2 + 2L * 2) = 5(L + -7) + 32 -21 + 3L + (10 + 4L) = 5(L + -7) + 32 Reorder the terms: -21 + 10 + 3L + 4L = 5(L + -7) + 32 Combine like terms: -21 + 10 = -11 -11 + 3L + 4L = 5(L + -7) + 32 Combine like terms: 3L + 4L = 7L -11 + 7L = 5(L + -7) + 32 Reorder the terms: -11 + 7L = 5(-7 + L) + 32 -11 + 7L = (-7 * 5 + L * 5) + 32 -11 + 7L = (-35 + 5L) + 32 Reorder the terms: -11 + 7L = -35 + 32 + 5L Combine like terms: -35 + 32 = -3 -11 + 7L = -3 + 5L Solving -11 + 7L = -3 + 5L Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '-5L' to each side of the equation. -11 + 7L + -5L = -3 + 5L + -5L Combine like terms: 7L + -5L = 2L -11 + 2L = -3 + 5L + -5L Combine like terms: 5L + -5L = 0 -11 + 2L = -3 + 0 -11 + 2L = -3 Add '11' to each side of the equation. -11 + 11 + 2L = -3 + 11 Combine like terms: -11 + 11 = 0 0 + 2L = -3 + 11 2L = -3 + 11 Combine like terms: -3 + 11 = 8 2L = 8 Divide each side by '2'. L = 4 Simplifying L = 4
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