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Simplifying -31 = -7(a + 7) + 8(4a + -4) Reorder the terms: -31 = -7(7 + a) + 8(4a + -4) -31 = (7 * -7 + a * -7) + 8(4a + -4) -31 = (-49 + -7a) + 8(4a + -4) Reorder the terms: -31 = -49 + -7a + 8(-4 + 4a) -31 = -49 + -7a + (-4 * 8 + 4a * 8) -31 = -49 + -7a + (-32 + 32a) Reorder the terms: -31 = -49 + -32 + -7a + 32a Combine like terms: -49 + -32 = -81 -31 = -81 + -7a + 32a Combine like terms: -7a + 32a = 25a -31 = -81 + 25a Solving -31 = -81 + 25a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-25a' to each side of the equation. -31 + -25a = -81 + 25a + -25a Combine like terms: 25a + -25a = 0 -31 + -25a = -81 + 0 -31 + -25a = -81 Add '31' to each side of the equation. -31 + 31 + -25a = -81 + 31 Combine like terms: -31 + 31 = 0 0 + -25a = -81 + 31 -25a = -81 + 31 Combine like terms: -81 + 31 = -50 -25a = -50 Divide each side by '-25'. a = 2 Simplifying a = 2
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