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Simplifying 7 = 8(1 + 2r) + -5(1 + 3r) 7 = (1 * 8 + 2r * 8) + -5(1 + 3r) 7 = (8 + 16r) + -5(1 + 3r) 7 = 8 + 16r + (1 * -5 + 3r * -5) 7 = 8 + 16r + (-5 + -15r) Reorder the terms: 7 = 8 + -5 + 16r + -15r Combine like terms: 8 + -5 = 3 7 = 3 + 16r + -15r Combine like terms: 16r + -15r = 1r 7 = 3 + 1r Solving 7 = 3 + 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. 7 + -1r = 3 + 1r + -1r Combine like terms: 1r + -1r = 0 7 + -1r = 3 + 0 7 + -1r = 3 Add '-7' to each side of the equation. 7 + -7 + -1r = 3 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 3 + -7 -1r = 3 + -7 Combine like terms: 3 + -7 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4
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