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Simplifying 4(a + -5) + -3(2a + 1) = 8(a + 2) + 3 Reorder the terms: 4(-5 + a) + -3(2a + 1) = 8(a + 2) + 3 (-5 * 4 + a * 4) + -3(2a + 1) = 8(a + 2) + 3 (-20 + 4a) + -3(2a + 1) = 8(a + 2) + 3 Reorder the terms: -20 + 4a + -3(1 + 2a) = 8(a + 2) + 3 -20 + 4a + (1 * -3 + 2a * -3) = 8(a + 2) + 3 -20 + 4a + (-3 + -6a) = 8(a + 2) + 3 Reorder the terms: -20 + -3 + 4a + -6a = 8(a + 2) + 3 Combine like terms: -20 + -3 = -23 -23 + 4a + -6a = 8(a + 2) + 3 Combine like terms: 4a + -6a = -2a -23 + -2a = 8(a + 2) + 3 Reorder the terms: -23 + -2a = 8(2 + a) + 3 -23 + -2a = (2 * 8 + a * 8) + 3 -23 + -2a = (16 + 8a) + 3 Reorder the terms: -23 + -2a = 16 + 3 + 8a Combine like terms: 16 + 3 = 19 -23 + -2a = 19 + 8a Solving -23 + -2a = 19 + 8a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8a' to each side of the equation. -23 + -2a + -8a = 19 + 8a + -8a Combine like terms: -2a + -8a = -10a -23 + -10a = 19 + 8a + -8a Combine like terms: 8a + -8a = 0 -23 + -10a = 19 + 0 -23 + -10a = 19 Add '23' to each side of the equation. -23 + 23 + -10a = 19 + 23 Combine like terms: -23 + 23 = 0 0 + -10a = 19 + 23 -10a = 19 + 23 Combine like terms: 19 + 23 = 42 -10a = 42 Divide each side by '-10'. a = -4.2 Simplifying a = -4.2
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