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Simplifying 19 + -7a = 4(a + 6) + -8(5 + 2a) Reorder the terms: 19 + -7a = 4(6 + a) + -8(5 + 2a) 19 + -7a = (6 * 4 + a * 4) + -8(5 + 2a) 19 + -7a = (24 + 4a) + -8(5 + 2a) 19 + -7a = 24 + 4a + (5 * -8 + 2a * -8) 19 + -7a = 24 + 4a + (-40 + -16a) Reorder the terms: 19 + -7a = 24 + -40 + 4a + -16a Combine like terms: 24 + -40 = -16 19 + -7a = -16 + 4a + -16a Combine like terms: 4a + -16a = -12a 19 + -7a = -16 + -12a Solving 19 + -7a = -16 + -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. 19 + -7a + 12a = -16 + -12a + 12a Combine like terms: -7a + 12a = 5a 19 + 5a = -16 + -12a + 12a Combine like terms: -12a + 12a = 0 19 + 5a = -16 + 0 19 + 5a = -16 Add '-19' to each side of the equation. 19 + -19 + 5a = -16 + -19 Combine like terms: 19 + -19 = 0 0 + 5a = -16 + -19 5a = -16 + -19 Combine like terms: -16 + -19 = -35 5a = -35 Divide each side by '5'. a = -7 Simplifying a = -7
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