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Simplifying 8(2 + -3b) + 6(4b + -3) = 4(4b + 3) + -3(5b + 2) (2 * 8 + -3b * 8) + 6(4b + -3) = 4(4b + 3) + -3(5b + 2) (16 + -24b) + 6(4b + -3) = 4(4b + 3) + -3(5b + 2) Reorder the terms: 16 + -24b + 6(-3 + 4b) = 4(4b + 3) + -3(5b + 2) 16 + -24b + (-3 * 6 + 4b * 6) = 4(4b + 3) + -3(5b + 2) 16 + -24b + (-18 + 24b) = 4(4b + 3) + -3(5b + 2) Reorder the terms: 16 + -18 + -24b + 24b = 4(4b + 3) + -3(5b + 2) Combine like terms: 16 + -18 = -2 -2 + -24b + 24b = 4(4b + 3) + -3(5b + 2) Combine like terms: -24b + 24b = 0 -2 + 0 = 4(4b + 3) + -3(5b + 2) -2 = 4(4b + 3) + -3(5b + 2) Reorder the terms: -2 = 4(3 + 4b) + -3(5b + 2) -2 = (3 * 4 + 4b * 4) + -3(5b + 2) -2 = (12 + 16b) + -3(5b + 2) Reorder the terms: -2 = 12 + 16b + -3(2 + 5b) -2 = 12 + 16b + (2 * -3 + 5b * -3) -2 = 12 + 16b + (-6 + -15b) Reorder the terms: -2 = 12 + -6 + 16b + -15b Combine like terms: 12 + -6 = 6 -2 = 6 + 16b + -15b Combine like terms: 16b + -15b = 1b -2 = 6 + 1b Solving -2 = 6 + 1b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1b' to each side of the equation. -2 + -1b = 6 + 1b + -1b Combine like terms: 1b + -1b = 0 -2 + -1b = 6 + 0 -2 + -1b = 6 Add '2' to each side of the equation. -2 + 2 + -1b = 6 + 2 Combine like terms: -2 + 2 = 0 0 + -1b = 6 + 2 -1b = 6 + 2 Combine like terms: 6 + 2 = 8 -1b = 8 Divide each side by '-1'. b = -8 Simplifying b = -8
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