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Simplifying 7 + -10(1 + -10a) = 11a + 8(9a + -11) 7 + (1 * -10 + -10a * -10) = 11a + 8(9a + -11) 7 + (-10 + 100a) = 11a + 8(9a + -11) Combine like terms: 7 + -10 = -3 -3 + 100a = 11a + 8(9a + -11) Reorder the terms: -3 + 100a = 11a + 8(-11 + 9a) -3 + 100a = 11a + (-11 * 8 + 9a * 8) -3 + 100a = 11a + (-88 + 72a) Reorder the terms: -3 + 100a = -88 + 11a + 72a Combine like terms: 11a + 72a = 83a -3 + 100a = -88 + 83a Solving -3 + 100a = -88 + 83a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-83a' to each side of the equation. -3 + 100a + -83a = -88 + 83a + -83a Combine like terms: 100a + -83a = 17a -3 + 17a = -88 + 83a + -83a Combine like terms: 83a + -83a = 0 -3 + 17a = -88 + 0 -3 + 17a = -88 Add '3' to each side of the equation. -3 + 3 + 17a = -88 + 3 Combine like terms: -3 + 3 = 0 0 + 17a = -88 + 3 17a = -88 + 3 Combine like terms: -88 + 3 = -85 17a = -85 Divide each side by '17'. a = -5 Simplifying a = -5
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