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Simplifying -47 = 6(7n + -2) + -7(n + -5) Reorder the terms: -47 = 6(-2 + 7n) + -7(n + -5) -47 = (-2 * 6 + 7n * 6) + -7(n + -5) -47 = (-12 + 42n) + -7(n + -5) Reorder the terms: -47 = -12 + 42n + -7(-5 + n) -47 = -12 + 42n + (-5 * -7 + n * -7) -47 = -12 + 42n + (35 + -7n) Reorder the terms: -47 = -12 + 35 + 42n + -7n Combine like terms: -12 + 35 = 23 -47 = 23 + 42n + -7n Combine like terms: 42n + -7n = 35n -47 = 23 + 35n Solving -47 = 23 + 35n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-35n' to each side of the equation. -47 + -35n = 23 + 35n + -35n Combine like terms: 35n + -35n = 0 -47 + -35n = 23 + 0 -47 + -35n = 23 Add '47' to each side of the equation. -47 + 47 + -35n = 23 + 47 Combine like terms: -47 + 47 = 0 0 + -35n = 23 + 47 -35n = 23 + 47 Combine like terms: 23 + 47 = 70 -35n = 70 Divide each side by '-35'. n = -2 Simplifying n = -2
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