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Simplifying 7(1 + 3a) + -7(a + -5) = 2a + -6 + -4a (1 * 7 + 3a * 7) + -7(a + -5) = 2a + -6 + -4a (7 + 21a) + -7(a + -5) = 2a + -6 + -4a Reorder the terms: 7 + 21a + -7(-5 + a) = 2a + -6 + -4a 7 + 21a + (-5 * -7 + a * -7) = 2a + -6 + -4a 7 + 21a + (35 + -7a) = 2a + -6 + -4a Reorder the terms: 7 + 35 + 21a + -7a = 2a + -6 + -4a Combine like terms: 7 + 35 = 42 42 + 21a + -7a = 2a + -6 + -4a Combine like terms: 21a + -7a = 14a 42 + 14a = 2a + -6 + -4a Reorder the terms: 42 + 14a = -6 + 2a + -4a Combine like terms: 2a + -4a = -2a 42 + 14a = -6 + -2a Solving 42 + 14a = -6 + -2a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2a' to each side of the equation. 42 + 14a + 2a = -6 + -2a + 2a Combine like terms: 14a + 2a = 16a 42 + 16a = -6 + -2a + 2a Combine like terms: -2a + 2a = 0 42 + 16a = -6 + 0 42 + 16a = -6 Add '-42' to each side of the equation. 42 + -42 + 16a = -6 + -42 Combine like terms: 42 + -42 = 0 0 + 16a = -6 + -42 16a = -6 + -42 Combine like terms: -6 + -42 = -48 16a = -48 Divide each side by '16'. a = -3 Simplifying a = -3
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