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Simplifying 8(a + -3) + 6(2a + -1) = 8(4a + -2) + -2(6a + 7) Reorder the terms: 8(-3 + a) + 6(2a + -1) = 8(4a + -2) + -2(6a + 7) (-3 * 8 + a * 8) + 6(2a + -1) = 8(4a + -2) + -2(6a + 7) (-24 + 8a) + 6(2a + -1) = 8(4a + -2) + -2(6a + 7) Reorder the terms: -24 + 8a + 6(-1 + 2a) = 8(4a + -2) + -2(6a + 7) -24 + 8a + (-1 * 6 + 2a * 6) = 8(4a + -2) + -2(6a + 7) -24 + 8a + (-6 + 12a) = 8(4a + -2) + -2(6a + 7) Reorder the terms: -24 + -6 + 8a + 12a = 8(4a + -2) + -2(6a + 7) Combine like terms: -24 + -6 = -30 -30 + 8a + 12a = 8(4a + -2) + -2(6a + 7) Combine like terms: 8a + 12a = 20a -30 + 20a = 8(4a + -2) + -2(6a + 7) Reorder the terms: -30 + 20a = 8(-2 + 4a) + -2(6a + 7) -30 + 20a = (-2 * 8 + 4a * 8) + -2(6a + 7) -30 + 20a = (-16 + 32a) + -2(6a + 7) Reorder the terms: -30 + 20a = -16 + 32a + -2(7 + 6a) -30 + 20a = -16 + 32a + (7 * -2 + 6a * -2) -30 + 20a = -16 + 32a + (-14 + -12a) Reorder the terms: -30 + 20a = -16 + -14 + 32a + -12a Combine like terms: -16 + -14 = -30 -30 + 20a = -30 + 32a + -12a Combine like terms: 32a + -12a = 20a -30 + 20a = -30 + 20a Add '30' to each side of the equation. -30 + 30 + 20a = -30 + 30 + 20a Combine like terms: -30 + 30 = 0 0 + 20a = -30 + 30 + 20a 20a = -30 + 30 + 20a Combine like terms: -30 + 30 = 0 20a = 0 + 20a 20a = 20a Add '-20a' to each side of the equation. 20a + -20a = 20a + -20a Combine like terms: 20a + -20a = 0 0 = 20a + -20a Combine like terms: 20a + -20a = 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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