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Simplifying 5(7 + -5(6 + -1a)) + -7 = 7(5(7a + -6) + 4) 5(7 + (6 * -5 + -1a * -5)) + -7 = 7(5(7a + -6) + 4) 5(7 + (-30 + 5a)) + -7 = 7(5(7a + -6) + 4) Combine like terms: 7 + -30 = -23 5(-23 + 5a) + -7 = 7(5(7a + -6) + 4) (-23 * 5 + 5a * 5) + -7 = 7(5(7a + -6) + 4) (-115 + 25a) + -7 = 7(5(7a + -6) + 4) Reorder the terms: -115 + -7 + 25a = 7(5(7a + -6) + 4) Combine like terms: -115 + -7 = -122 -122 + 25a = 7(5(7a + -6) + 4) Reorder the terms: -122 + 25a = 7(5(-6 + 7a) + 4) -122 + 25a = 7((-6 * 5 + 7a * 5) + 4) -122 + 25a = 7((-30 + 35a) + 4) Reorder the terms: -122 + 25a = 7(-30 + 4 + 35a) Combine like terms: -30 + 4 = -26 -122 + 25a = 7(-26 + 35a) -122 + 25a = (-26 * 7 + 35a * 7) -122 + 25a = (-182 + 245a) Solving -122 + 25a = -182 + 245a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-245a' to each side of the equation. -122 + 25a + -245a = -182 + 245a + -245a Combine like terms: 25a + -245a = -220a -122 + -220a = -182 + 245a + -245a Combine like terms: 245a + -245a = 0 -122 + -220a = -182 + 0 -122 + -220a = -182 Add '122' to each side of the equation. -122 + 122 + -220a = -182 + 122 Combine like terms: -122 + 122 = 0 0 + -220a = -182 + 122 -220a = -182 + 122 Combine like terms: -182 + 122 = -60 -220a = -60 Divide each side by '-220'. a = 0.2727272727 Simplifying a = 0.2727272727
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