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Simplifying 4[5(2w + 3) + -1(8w + 7)] = 2(4w + 9) + 14 Reorder the terms: 4[5(3 + 2w) + -1(8w + 7)] = 2(4w + 9) + 14 4[(3 * 5 + 2w * 5) + -1(8w + 7)] = 2(4w + 9) + 14 4[(15 + 10w) + -1(8w + 7)] = 2(4w + 9) + 14 Reorder the terms: 4[15 + 10w + -1(7 + 8w)] = 2(4w + 9) + 14 4[15 + 10w + (7 * -1 + 8w * -1)] = 2(4w + 9) + 14 4[15 + 10w + (-7 + -8w)] = 2(4w + 9) + 14 Reorder the terms: 4[15 + -7 + 10w + -8w] = 2(4w + 9) + 14 Combine like terms: 15 + -7 = 8 4[8 + 10w + -8w] = 2(4w + 9) + 14 Combine like terms: 10w + -8w = 2w 4[8 + 2w] = 2(4w + 9) + 14 [8 * 4 + 2w * 4] = 2(4w + 9) + 14 [32 + 8w] = 2(4w + 9) + 14 Reorder the terms: 32 + 8w = 2(9 + 4w) + 14 32 + 8w = (9 * 2 + 4w * 2) + 14 32 + 8w = (18 + 8w) + 14 Reorder the terms: 32 + 8w = 18 + 14 + 8w Combine like terms: 18 + 14 = 32 32 + 8w = 32 + 8w Add '-32' to each side of the equation. 32 + -32 + 8w = 32 + -32 + 8w Combine like terms: 32 + -32 = 0 0 + 8w = 32 + -32 + 8w 8w = 32 + -32 + 8w Combine like terms: 32 + -32 = 0 8w = 0 + 8w 8w = 8w Add '-8w' to each side of the equation. 8w + -8w = 8w + -8w Combine like terms: 8w + -8w = 0 0 = 8w + -8w Combine like terms: 8w + -8w = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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