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Simplifying -2(a + -8) + 7 = 5(a + 2) + -3a + -19 Reorder the terms: -2(-8 + a) + 7 = 5(a + 2) + -3a + -19 (-8 * -2 + a * -2) + 7 = 5(a + 2) + -3a + -19 (16 + -2a) + 7 = 5(a + 2) + -3a + -19 Reorder the terms: 16 + 7 + -2a = 5(a + 2) + -3a + -19 Combine like terms: 16 + 7 = 23 23 + -2a = 5(a + 2) + -3a + -19 Reorder the terms: 23 + -2a = 5(2 + a) + -3a + -19 23 + -2a = (2 * 5 + a * 5) + -3a + -19 23 + -2a = (10 + 5a) + -3a + -19 Reorder the terms: 23 + -2a = 10 + -19 + 5a + -3a Combine like terms: 10 + -19 = -9 23 + -2a = -9 + 5a + -3a Combine like terms: 5a + -3a = 2a 23 + -2a = -9 + 2a Solving 23 + -2a = -9 + 2a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 23 + -2a + -2a = -9 + 2a + -2a Combine like terms: -2a + -2a = -4a 23 + -4a = -9 + 2a + -2a Combine like terms: 2a + -2a = 0 23 + -4a = -9 + 0 23 + -4a = -9 Add '-23' to each side of the equation. 23 + -23 + -4a = -9 + -23 Combine like terms: 23 + -23 = 0 0 + -4a = -9 + -23 -4a = -9 + -23 Combine like terms: -9 + -23 = -32 -4a = -32 Divide each side by '-4'. a = 8 Simplifying a = 8
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