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Simplifying 7(a + -4) + 2c = 19 + 3(a + 3) Reorder the terms: 7(-4 + a) + 2c = 19 + 3(a + 3) (-4 * 7 + a * 7) + 2c = 19 + 3(a + 3) (-28 + 7a) + 2c = 19 + 3(a + 3) Reorder the terms: -28 + 7a + 2c = 19 + 3(3 + a) -28 + 7a + 2c = 19 + (3 * 3 + a * 3) -28 + 7a + 2c = 19 + (9 + 3a) Combine like terms: 19 + 9 = 28 -28 + 7a + 2c = 28 + 3a Solving -28 + 7a + 2c = 28 + 3a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3a' to each side of the equation. -28 + 7a + -3a + 2c = 28 + 3a + -3a Combine like terms: 7a + -3a = 4a -28 + 4a + 2c = 28 + 3a + -3a Combine like terms: 3a + -3a = 0 -28 + 4a + 2c = 28 + 0 -28 + 4a + 2c = 28 Add '28' to each side of the equation. -28 + 4a + 28 + 2c = 28 + 28 Reorder the terms: -28 + 28 + 4a + 2c = 28 + 28 Combine like terms: -28 + 28 = 0 0 + 4a + 2c = 28 + 28 4a + 2c = 28 + 28 Combine like terms: 28 + 28 = 56 4a + 2c = 56 Add '-2c' to each side of the equation. 4a + 2c + -2c = 56 + -2c Combine like terms: 2c + -2c = 0 4a + 0 = 56 + -2c 4a = 56 + -2c Divide each side by '4'. a = 14 + -0.5c Simplifying a = 14 + -0.5c
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