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Simplifying 0.75(4a + -1) + -5 = 0.25(3 + -2a) + 11 Reorder the terms: 0.75(-1 + 4a) + -5 = 0.25(3 + -2a) + 11 (-1 * 0.75 + 4a * 0.75) + -5 = 0.25(3 + -2a) + 11 (-0.75 + 3a) + -5 = 0.25(3 + -2a) + 11 Reorder the terms: -0.75 + -5 + 3a = 0.25(3 + -2a) + 11 Combine like terms: -0.75 + -5 = -5.75 -5.75 + 3a = 0.25(3 + -2a) + 11 -5.75 + 3a = (3 * 0.25 + -2a * 0.25) + 11 -5.75 + 3a = (0.75 + -0.5a) + 11 Reorder the terms: -5.75 + 3a = 0.75 + 11 + -0.5a Combine like terms: 0.75 + 11 = 11.75 -5.75 + 3a = 11.75 + -0.5a Solving -5.75 + 3a = 11.75 + -0.5a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5a' to each side of the equation. -5.75 + 3a + 0.5a = 11.75 + -0.5a + 0.5a Combine like terms: 3a + 0.5a = 3.5a -5.75 + 3.5a = 11.75 + -0.5a + 0.5a Combine like terms: -0.5a + 0.5a = 0.0 -5.75 + 3.5a = 11.75 + 0.0 -5.75 + 3.5a = 11.75 Add '5.75' to each side of the equation. -5.75 + 5.75 + 3.5a = 11.75 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 3.5a = 11.75 + 5.75 3.5a = 11.75 + 5.75 Combine like terms: 11.75 + 5.75 = 17.5 3.5a = 17.5 Divide each side by '3.5'. a = 5 Simplifying a = 5
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