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Simplifying 7 + 4r + -7r = -3(-1r + 1) + 2(-4 + 6r) Combine like terms: 4r + -7r = -3r 7 + -3r = -3(-1r + 1) + 2(-4 + 6r) Reorder the terms: 7 + -3r = -3(1 + -1r) + 2(-4 + 6r) 7 + -3r = (1 * -3 + -1r * -3) + 2(-4 + 6r) 7 + -3r = (-3 + 3r) + 2(-4 + 6r) 7 + -3r = -3 + 3r + (-4 * 2 + 6r * 2) 7 + -3r = -3 + 3r + (-8 + 12r) Reorder the terms: 7 + -3r = -3 + -8 + 3r + 12r Combine like terms: -3 + -8 = -11 7 + -3r = -11 + 3r + 12r Combine like terms: 3r + 12r = 15r 7 + -3r = -11 + 15r Solving 7 + -3r = -11 + 15r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15r' to each side of the equation. 7 + -3r + -15r = -11 + 15r + -15r Combine like terms: -3r + -15r = -18r 7 + -18r = -11 + 15r + -15r Combine like terms: 15r + -15r = 0 7 + -18r = -11 + 0 7 + -18r = -11 Add '-7' to each side of the equation. 7 + -7 + -18r = -11 + -7 Combine like terms: 7 + -7 = 0 0 + -18r = -11 + -7 -18r = -11 + -7 Combine like terms: -11 + -7 = -18 -18r = -18 Divide each side by '-18'. r = 1 Simplifying r = 1
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