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Simplifying 5(2a + 1) + 3(3a + -4) = 4(3a + -6) Reorder the terms: 5(1 + 2a) + 3(3a + -4) = 4(3a + -6) (1 * 5 + 2a * 5) + 3(3a + -4) = 4(3a + -6) (5 + 10a) + 3(3a + -4) = 4(3a + -6) Reorder the terms: 5 + 10a + 3(-4 + 3a) = 4(3a + -6) 5 + 10a + (-4 * 3 + 3a * 3) = 4(3a + -6) 5 + 10a + (-12 + 9a) = 4(3a + -6) Reorder the terms: 5 + -12 + 10a + 9a = 4(3a + -6) Combine like terms: 5 + -12 = -7 -7 + 10a + 9a = 4(3a + -6) Combine like terms: 10a + 9a = 19a -7 + 19a = 4(3a + -6) Reorder the terms: -7 + 19a = 4(-6 + 3a) -7 + 19a = (-6 * 4 + 3a * 4) -7 + 19a = (-24 + 12a) Solving -7 + 19a = -24 + 12a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12a' to each side of the equation. -7 + 19a + -12a = -24 + 12a + -12a Combine like terms: 19a + -12a = 7a -7 + 7a = -24 + 12a + -12a Combine like terms: 12a + -12a = 0 -7 + 7a = -24 + 0 -7 + 7a = -24 Add '7' to each side of the equation. -7 + 7 + 7a = -24 + 7 Combine like terms: -7 + 7 = 0 0 + 7a = -24 + 7 7a = -24 + 7 Combine like terms: -24 + 7 = -17 7a = -17 Divide each side by '7'. a = -2.428571429 Simplifying a = -2.428571429
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