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Simplifying -42 = 7(3r + 7) + 7(r + -1) Reorder the terms: -42 = 7(7 + 3r) + 7(r + -1) -42 = (7 * 7 + 3r * 7) + 7(r + -1) -42 = (49 + 21r) + 7(r + -1) Reorder the terms: -42 = 49 + 21r + 7(-1 + r) -42 = 49 + 21r + (-1 * 7 + r * 7) -42 = 49 + 21r + (-7 + 7r) Reorder the terms: -42 = 49 + -7 + 21r + 7r Combine like terms: 49 + -7 = 42 -42 = 42 + 21r + 7r Combine like terms: 21r + 7r = 28r -42 = 42 + 28r Solving -42 = 42 + 28r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-28r' to each side of the equation. -42 + -28r = 42 + 28r + -28r Combine like terms: 28r + -28r = 0 -42 + -28r = 42 + 0 -42 + -28r = 42 Add '42' to each side of the equation. -42 + 42 + -28r = 42 + 42 Combine like terms: -42 + 42 = 0 0 + -28r = 42 + 42 -28r = 42 + 42 Combine like terms: 42 + 42 = 84 -28r = 84 Divide each side by '-28'. r = -3 Simplifying r = -3
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