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Simplifying 4(3a + -1) = 5(4a + -1) + -4(3a + 2) Reorder the terms: 4(-1 + 3a) = 5(4a + -1) + -4(3a + 2) (-1 * 4 + 3a * 4) = 5(4a + -1) + -4(3a + 2) (-4 + 12a) = 5(4a + -1) + -4(3a + 2) Reorder the terms: -4 + 12a = 5(-1 + 4a) + -4(3a + 2) -4 + 12a = (-1 * 5 + 4a * 5) + -4(3a + 2) -4 + 12a = (-5 + 20a) + -4(3a + 2) Reorder the terms: -4 + 12a = -5 + 20a + -4(2 + 3a) -4 + 12a = -5 + 20a + (2 * -4 + 3a * -4) -4 + 12a = -5 + 20a + (-8 + -12a) Reorder the terms: -4 + 12a = -5 + -8 + 20a + -12a Combine like terms: -5 + -8 = -13 -4 + 12a = -13 + 20a + -12a Combine like terms: 20a + -12a = 8a -4 + 12a = -13 + 8a Solving -4 + 12a = -13 + 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. -4 + 12a + -8a = -13 + 8a + -8a Combine like terms: 12a + -8a = 4a -4 + 4a = -13 + 8a + -8a Combine like terms: 8a + -8a = 0 -4 + 4a = -13 + 0 -4 + 4a = -13 Add '4' to each side of the equation. -4 + 4 + 4a = -13 + 4 Combine like terms: -4 + 4 = 0 0 + 4a = -13 + 4 4a = -13 + 4 Combine like terms: -13 + 4 = -9 4a = -9 Divide each side by '4'. a = -2.25 Simplifying a = -2.25
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