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Simplifying -5(3v + 18) = 7(v + 6) + 1(v + 6) Reorder the terms: -5(18 + 3v) = 7(v + 6) + 1(v + 6) (18 * -5 + 3v * -5) = 7(v + 6) + 1(v + 6) (-90 + -15v) = 7(v + 6) + 1(v + 6) Reorder the terms: -90 + -15v = 7(6 + v) + 1(v + 6) -90 + -15v = (6 * 7 + v * 7) + 1(v + 6) -90 + -15v = (42 + 7v) + 1(v + 6) Reorder the terms: -90 + -15v = 42 + 7v + 1(6 + v) -90 + -15v = 42 + 7v + (6 * 1 + v * 1) -90 + -15v = 42 + 7v + (6 + 1v) Reorder the terms: -90 + -15v = 42 + 6 + 7v + 1v Combine like terms: 42 + 6 = 48 -90 + -15v = 48 + 7v + 1v Combine like terms: 7v + 1v = 8v -90 + -15v = 48 + 8v Solving -90 + -15v = 48 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. -90 + -15v + -8v = 48 + 8v + -8v Combine like terms: -15v + -8v = -23v -90 + -23v = 48 + 8v + -8v Combine like terms: 8v + -8v = 0 -90 + -23v = 48 + 0 -90 + -23v = 48 Add '90' to each side of the equation. -90 + 90 + -23v = 48 + 90 Combine like terms: -90 + 90 = 0 0 + -23v = 48 + 90 -23v = 48 + 90 Combine like terms: 48 + 90 = 138 -23v = 138 Divide each side by '-23'. v = -6 Simplifying v = -6
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