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Simplifying 7(-5r + -5) + -8 = 4(1 + 5r) + -8r Reorder the terms: 7(-5 + -5r) + -8 = 4(1 + 5r) + -8r (-5 * 7 + -5r * 7) + -8 = 4(1 + 5r) + -8r (-35 + -35r) + -8 = 4(1 + 5r) + -8r Reorder the terms: -35 + -8 + -35r = 4(1 + 5r) + -8r Combine like terms: -35 + -8 = -43 -43 + -35r = 4(1 + 5r) + -8r -43 + -35r = (1 * 4 + 5r * 4) + -8r -43 + -35r = (4 + 20r) + -8r Combine like terms: 20r + -8r = 12r -43 + -35r = 4 + 12r Solving -43 + -35r = 4 + 12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. -43 + -35r + -12r = 4 + 12r + -12r Combine like terms: -35r + -12r = -47r -43 + -47r = 4 + 12r + -12r Combine like terms: 12r + -12r = 0 -43 + -47r = 4 + 0 -43 + -47r = 4 Add '43' to each side of the equation. -43 + 43 + -47r = 4 + 43 Combine like terms: -43 + 43 = 0 0 + -47r = 4 + 43 -47r = 4 + 43 Combine like terms: 4 + 43 = 47 -47r = 47 Divide each side by '-47'. r = -1 Simplifying r = -1
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