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Simplifying 3(4a + -3) + -1(4a + -4) = 7 + -1(5a + -1) Reorder the terms: 3(-3 + 4a) + -1(4a + -4) = 7 + -1(5a + -1) (-3 * 3 + 4a * 3) + -1(4a + -4) = 7 + -1(5a + -1) (-9 + 12a) + -1(4a + -4) = 7 + -1(5a + -1) Reorder the terms: -9 + 12a + -1(-4 + 4a) = 7 + -1(5a + -1) -9 + 12a + (-4 * -1 + 4a * -1) = 7 + -1(5a + -1) -9 + 12a + (4 + -4a) = 7 + -1(5a + -1) Reorder the terms: -9 + 4 + 12a + -4a = 7 + -1(5a + -1) Combine like terms: -9 + 4 = -5 -5 + 12a + -4a = 7 + -1(5a + -1) Combine like terms: 12a + -4a = 8a -5 + 8a = 7 + -1(5a + -1) Reorder the terms: -5 + 8a = 7 + -1(-1 + 5a) -5 + 8a = 7 + (-1 * -1 + 5a * -1) -5 + 8a = 7 + (1 + -5a) Combine like terms: 7 + 1 = 8 -5 + 8a = 8 + -5a Solving -5 + 8a = 8 + -5a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5a' to each side of the equation. -5 + 8a + 5a = 8 + -5a + 5a Combine like terms: 8a + 5a = 13a -5 + 13a = 8 + -5a + 5a Combine like terms: -5a + 5a = 0 -5 + 13a = 8 + 0 -5 + 13a = 8 Add '5' to each side of the equation. -5 + 5 + 13a = 8 + 5 Combine like terms: -5 + 5 = 0 0 + 13a = 8 + 5 13a = 8 + 5 Combine like terms: 8 + 5 = 13 13a = 13 Divide each side by '13'. a = 1 Simplifying a = 1
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