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Simplifying 5(a + -3) + -4(a + 2) = 2 + 3(1 + -2a) Reorder the terms: 5(-3 + a) + -4(a + 2) = 2 + 3(1 + -2a) (-3 * 5 + a * 5) + -4(a + 2) = 2 + 3(1 + -2a) (-15 + 5a) + -4(a + 2) = 2 + 3(1 + -2a) Reorder the terms: -15 + 5a + -4(2 + a) = 2 + 3(1 + -2a) -15 + 5a + (2 * -4 + a * -4) = 2 + 3(1 + -2a) -15 + 5a + (-8 + -4a) = 2 + 3(1 + -2a) Reorder the terms: -15 + -8 + 5a + -4a = 2 + 3(1 + -2a) Combine like terms: -15 + -8 = -23 -23 + 5a + -4a = 2 + 3(1 + -2a) Combine like terms: 5a + -4a = 1a -23 + 1a = 2 + 3(1 + -2a) -23 + 1a = 2 + (1 * 3 + -2a * 3) -23 + 1a = 2 + (3 + -6a) Combine like terms: 2 + 3 = 5 -23 + 1a = 5 + -6a Solving -23 + 1a = 5 + -6a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6a' to each side of the equation. -23 + 1a + 6a = 5 + -6a + 6a Combine like terms: 1a + 6a = 7a -23 + 7a = 5 + -6a + 6a Combine like terms: -6a + 6a = 0 -23 + 7a = 5 + 0 -23 + 7a = 5 Add '23' to each side of the equation. -23 + 23 + 7a = 5 + 23 Combine like terms: -23 + 23 = 0 0 + 7a = 5 + 23 7a = 5 + 23 Combine like terms: 5 + 23 = 28 7a = 28 Divide each side by '7'. a = 4 Simplifying a = 4
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