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Simplifying 3(a + -1) + -1(5a + 4) = 5(2a + -4) + -23 Reorder the terms: 3(-1 + a) + -1(5a + 4) = 5(2a + -4) + -23 (-1 * 3 + a * 3) + -1(5a + 4) = 5(2a + -4) + -23 (-3 + 3a) + -1(5a + 4) = 5(2a + -4) + -23 Reorder the terms: -3 + 3a + -1(4 + 5a) = 5(2a + -4) + -23 -3 + 3a + (4 * -1 + 5a * -1) = 5(2a + -4) + -23 -3 + 3a + (-4 + -5a) = 5(2a + -4) + -23 Reorder the terms: -3 + -4 + 3a + -5a = 5(2a + -4) + -23 Combine like terms: -3 + -4 = -7 -7 + 3a + -5a = 5(2a + -4) + -23 Combine like terms: 3a + -5a = -2a -7 + -2a = 5(2a + -4) + -23 Reorder the terms: -7 + -2a = 5(-4 + 2a) + -23 -7 + -2a = (-4 * 5 + 2a * 5) + -23 -7 + -2a = (-20 + 10a) + -23 Reorder the terms: -7 + -2a = -20 + -23 + 10a Combine like terms: -20 + -23 = -43 -7 + -2a = -43 + 10a Solving -7 + -2a = -43 + 10a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10a' to each side of the equation. -7 + -2a + -10a = -43 + 10a + -10a Combine like terms: -2a + -10a = -12a -7 + -12a = -43 + 10a + -10a Combine like terms: 10a + -10a = 0 -7 + -12a = -43 + 0 -7 + -12a = -43 Add '7' to each side of the equation. -7 + 7 + -12a = -43 + 7 Combine like terms: -7 + 7 = 0 0 + -12a = -43 + 7 -12a = -43 + 7 Combine like terms: -43 + 7 = -36 -12a = -36 Divide each side by '-12'. a = 3 Simplifying a = 3
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