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Simplifying 29(a + -8) + 7 = 5(a + 2) + -3a + -19 Reorder the terms: 29(-8 + a) + 7 = 5(a + 2) + -3a + -19 (-8 * 29 + a * 29) + 7 = 5(a + 2) + -3a + -19 (-232 + 29a) + 7 = 5(a + 2) + -3a + -19 Reorder the terms: -232 + 7 + 29a = 5(a + 2) + -3a + -19 Combine like terms: -232 + 7 = -225 -225 + 29a = 5(a + 2) + -3a + -19 Reorder the terms: -225 + 29a = 5(2 + a) + -3a + -19 -225 + 29a = (2 * 5 + a * 5) + -3a + -19 -225 + 29a = (10 + 5a) + -3a + -19 Reorder the terms: -225 + 29a = 10 + -19 + 5a + -3a Combine like terms: 10 + -19 = -9 -225 + 29a = -9 + 5a + -3a Combine like terms: 5a + -3a = 2a -225 + 29a = -9 + 2a Solving -225 + 29a = -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. -225 + 29a + -2a = -9 + 2a + -2a Combine like terms: 29a + -2a = 27a -225 + 27a = -9 + 2a + -2a Combine like terms: 2a + -2a = 0 -225 + 27a = -9 + 0 -225 + 27a = -9 Add '225' to each side of the equation. -225 + 225 + 27a = -9 + 225 Combine like terms: -225 + 225 = 0 0 + 27a = -9 + 225 27a = -9 + 225 Combine like terms: -9 + 225 = 216 27a = 216 Divide each side by '27'. a = 8 Simplifying a = 8
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