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Simplifying -7(x + 5) + 10(a + 3) = a + 4 + 9 Reorder the terms: -7(5 + x) + 10(a + 3) = a + 4 + 9 (5 * -7 + x * -7) + 10(a + 3) = a + 4 + 9 (-35 + -7x) + 10(a + 3) = a + 4 + 9 Reorder the terms: -35 + -7x + 10(3 + a) = a + 4 + 9 -35 + -7x + (3 * 10 + a * 10) = a + 4 + 9 -35 + -7x + (30 + 10a) = a + 4 + 9 Reorder the terms: -35 + 30 + 10a + -7x = a + 4 + 9 Combine like terms: -35 + 30 = -5 -5 + 10a + -7x = a + 4 + 9 Reorder the terms: -5 + 10a + -7x = 4 + 9 + a Combine like terms: 4 + 9 = 13 -5 + 10a + -7x = 13 + a Solving -5 + 10a + -7x = 13 + a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1a' to each side of the equation. -5 + 10a + -1a + -7x = 13 + a + -1a Combine like terms: 10a + -1a = 9a -5 + 9a + -7x = 13 + a + -1a Combine like terms: a + -1a = 0 -5 + 9a + -7x = 13 + 0 -5 + 9a + -7x = 13 Add '5' to each side of the equation. -5 + 9a + 5 + -7x = 13 + 5 Reorder the terms: -5 + 5 + 9a + -7x = 13 + 5 Combine like terms: -5 + 5 = 0 0 + 9a + -7x = 13 + 5 9a + -7x = 13 + 5 Combine like terms: 13 + 5 = 18 9a + -7x = 18 Add '7x' to each side of the equation. 9a + -7x + 7x = 18 + 7x Combine like terms: -7x + 7x = 0 9a + 0 = 18 + 7x 9a = 18 + 7x Divide each side by '9'. a = 2 + 0.7777777778x Simplifying a = 2 + 0.7777777778x
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