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Simplifying 5(3a + -1) + -2(3a + 2) = 3(a + 2 + v) Reorder the terms: 5(-1 + 3a) + -2(3a + 2) = 3(a + 2 + v) (-1 * 5 + 3a * 5) + -2(3a + 2) = 3(a + 2 + v) (-5 + 15a) + -2(3a + 2) = 3(a + 2 + v) Reorder the terms: -5 + 15a + -2(2 + 3a) = 3(a + 2 + v) -5 + 15a + (2 * -2 + 3a * -2) = 3(a + 2 + v) -5 + 15a + (-4 + -6a) = 3(a + 2 + v) Reorder the terms: -5 + -4 + 15a + -6a = 3(a + 2 + v) Combine like terms: -5 + -4 = -9 -9 + 15a + -6a = 3(a + 2 + v) Combine like terms: 15a + -6a = 9a -9 + 9a = 3(a + 2 + v) Reorder the terms: -9 + 9a = 3(2 + a + v) -9 + 9a = (2 * 3 + a * 3 + v * 3) -9 + 9a = (6 + 3a + 3v) Solving -9 + 9a = 6 + 3a + 3v Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3a' to each side of the equation. -9 + 9a + -3a = 6 + 3a + -3a + 3v Combine like terms: 9a + -3a = 6a -9 + 6a = 6 + 3a + -3a + 3v Combine like terms: 3a + -3a = 0 -9 + 6a = 6 + 0 + 3v -9 + 6a = 6 + 3v Add '9' to each side of the equation. -9 + 9 + 6a = 6 + 9 + 3v Combine like terms: -9 + 9 = 0 0 + 6a = 6 + 9 + 3v 6a = 6 + 9 + 3v Combine like terms: 6 + 9 = 15 6a = 15 + 3v Divide each side by '6'. a = 2.5 + 0.5v Simplifying a = 2.5 + 0.5v
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