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Simplifying -53 = 5(a + 3) + 3(a + -4) Reorder the terms: -53 = 5(3 + a) + 3(a + -4) -53 = (3 * 5 + a * 5) + 3(a + -4) -53 = (15 + 5a) + 3(a + -4) Reorder the terms: -53 = 15 + 5a + 3(-4 + a) -53 = 15 + 5a + (-4 * 3 + a * 3) -53 = 15 + 5a + (-12 + 3a) Reorder the terms: -53 = 15 + -12 + 5a + 3a Combine like terms: 15 + -12 = 3 -53 = 3 + 5a + 3a Combine like terms: 5a + 3a = 8a -53 = 3 + 8a Solving -53 = 3 + 8a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8a' to each side of the equation. -53 + -8a = 3 + 8a + -8a Combine like terms: 8a + -8a = 0 -53 + -8a = 3 + 0 -53 + -8a = 3 Add '53' to each side of the equation. -53 + 53 + -8a = 3 + 53 Combine like terms: -53 + 53 = 0 0 + -8a = 3 + 53 -8a = 3 + 53 Combine like terms: 3 + 53 = 56 -8a = 56 Divide each side by '-8'. a = -7 Simplifying a = -7
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