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Simplifying 7(1 + 5n) + -8(6a + 5) = 32 (1 * 7 + 5n * 7) + -8(6a + 5) = 32 (7 + 35n) + -8(6a + 5) = 32 Reorder the terms: 7 + 35n + -8(5 + 6a) = 32 7 + 35n + (5 * -8 + 6a * -8) = 32 7 + 35n + (-40 + -48a) = 32 Reorder the terms: 7 + -40 + -48a + 35n = 32 Combine like terms: 7 + -40 = -33 -33 + -48a + 35n = 32 Solving -33 + -48a + 35n = 32 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '33' to each side of the equation. -33 + -48a + 33 + 35n = 32 + 33 Reorder the terms: -33 + 33 + -48a + 35n = 32 + 33 Combine like terms: -33 + 33 = 0 0 + -48a + 35n = 32 + 33 -48a + 35n = 32 + 33 Combine like terms: 32 + 33 = 65 -48a + 35n = 65 Add '-35n' to each side of the equation. -48a + 35n + -35n = 65 + -35n Combine like terms: 35n + -35n = 0 -48a + 0 = 65 + -35n -48a = 65 + -35n Divide each side by '-48'. a = -1.354166667 + 0.7291666667n Simplifying a = -1.354166667 + 0.7291666667n
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