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Simplifying 5r + 4(1 + r) = -6(-4r + 7) + 1 5r + (1 * 4 + r * 4) = -6(-4r + 7) + 1 5r + (4 + 4r) = -6(-4r + 7) + 1 Reorder the terms: 4 + 5r + 4r = -6(-4r + 7) + 1 Combine like terms: 5r + 4r = 9r 4 + 9r = -6(-4r + 7) + 1 Reorder the terms: 4 + 9r = -6(7 + -4r) + 1 4 + 9r = (7 * -6 + -4r * -6) + 1 4 + 9r = (-42 + 24r) + 1 Reorder the terms: 4 + 9r = -42 + 1 + 24r Combine like terms: -42 + 1 = -41 4 + 9r = -41 + 24r Solving 4 + 9r = -41 + 24r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-24r' to each side of the equation. 4 + 9r + -24r = -41 + 24r + -24r Combine like terms: 9r + -24r = -15r 4 + -15r = -41 + 24r + -24r Combine like terms: 24r + -24r = 0 4 + -15r = -41 + 0 4 + -15r = -41 Add '-4' to each side of the equation. 4 + -4 + -15r = -41 + -4 Combine like terms: 4 + -4 = 0 0 + -15r = -41 + -4 -15r = -41 + -4 Combine like terms: -41 + -4 = -45 -15r = -45 Divide each side by '-15'. r = 3 Simplifying r = 3
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