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Simplifying -47 = -4(1 + 7a) + 5(1 + 8a) -47 = (1 * -4 + 7a * -4) + 5(1 + 8a) -47 = (-4 + -28a) + 5(1 + 8a) -47 = -4 + -28a + (1 * 5 + 8a * 5) -47 = -4 + -28a + (5 + 40a) Reorder the terms: -47 = -4 + 5 + -28a + 40a Combine like terms: -4 + 5 = 1 -47 = 1 + -28a + 40a Combine like terms: -28a + 40a = 12a -47 = 1 + 12a Solving -47 = 1 + 12a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12a' to each side of the equation. -47 + -12a = 1 + 12a + -12a Combine like terms: 12a + -12a = 0 -47 + -12a = 1 + 0 -47 + -12a = 1 Add '47' to each side of the equation. -47 + 47 + -12a = 1 + 47 Combine like terms: -47 + 47 = 0 0 + -12a = 1 + 47 -12a = 1 + 47 Combine like terms: 1 + 47 = 48 -12a = 48 Divide each side by '-12'. a = -4 Simplifying a = -4
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