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Simplifying 5(7 + -1a) + -3(a + -4) + -4 = 4(a + -3) + 7 (7 * 5 + -1a * 5) + -3(a + -4) + -4 = 4(a + -3) + 7 (35 + -5a) + -3(a + -4) + -4 = 4(a + -3) + 7 Reorder the terms: 35 + -5a + -3(-4 + a) + -4 = 4(a + -3) + 7 35 + -5a + (-4 * -3 + a * -3) + -4 = 4(a + -3) + 7 35 + -5a + (12 + -3a) + -4 = 4(a + -3) + 7 Reorder the terms: 35 + 12 + -4 + -5a + -3a = 4(a + -3) + 7 Combine like terms: 35 + 12 = 47 47 + -4 + -5a + -3a = 4(a + -3) + 7 Combine like terms: 47 + -4 = 43 43 + -5a + -3a = 4(a + -3) + 7 Combine like terms: -5a + -3a = -8a 43 + -8a = 4(a + -3) + 7 Reorder the terms: 43 + -8a = 4(-3 + a) + 7 43 + -8a = (-3 * 4 + a * 4) + 7 43 + -8a = (-12 + 4a) + 7 Reorder the terms: 43 + -8a = -12 + 7 + 4a Combine like terms: -12 + 7 = -5 43 + -8a = -5 + 4a Solving 43 + -8a = -5 + 4a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4a' to each side of the equation. 43 + -8a + -4a = -5 + 4a + -4a Combine like terms: -8a + -4a = -12a 43 + -12a = -5 + 4a + -4a Combine like terms: 4a + -4a = 0 43 + -12a = -5 + 0 43 + -12a = -5 Add '-43' to each side of the equation. 43 + -43 + -12a = -5 + -43 Combine like terms: 43 + -43 = 0 0 + -12a = -5 + -43 -12a = -5 + -43 Combine like terms: -5 + -43 = -48 -12a = -48 Divide each side by '-12'. a = 4 Simplifying a = 4
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