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Simplifying 3 + 7(r + -3) = 23 + -1(5 + -1r) Reorder the terms: 3 + 7(-3 + r) = 23 + -1(5 + -1r) 3 + (-3 * 7 + r * 7) = 23 + -1(5 + -1r) 3 + (-21 + 7r) = 23 + -1(5 + -1r) Combine like terms: 3 + -21 = -18 -18 + 7r = 23 + -1(5 + -1r) -18 + 7r = 23 + (5 * -1 + -1r * -1) -18 + 7r = 23 + (-5 + 1r) Combine like terms: 23 + -5 = 18 -18 + 7r = 18 + 1r Solving -18 + 7r = 18 + 1r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1r' to each side of the equation. -18 + 7r + -1r = 18 + 1r + -1r Combine like terms: 7r + -1r = 6r -18 + 6r = 18 + 1r + -1r Combine like terms: 1r + -1r = 0 -18 + 6r = 18 + 0 -18 + 6r = 18 Add '18' to each side of the equation. -18 + 18 + 6r = 18 + 18 Combine like terms: -18 + 18 = 0 0 + 6r = 18 + 18 6r = 18 + 18 Combine like terms: 18 + 18 = 36 6r = 36 Divide each side by '6'. r = 6 Simplifying r = 6
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