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Simplifying 65 = 5(r + -3) + 6(4r + -6) Reorder the terms: 65 = 5(-3 + r) + 6(4r + -6) 65 = (-3 * 5 + r * 5) + 6(4r + -6) 65 = (-15 + 5r) + 6(4r + -6) Reorder the terms: 65 = -15 + 5r + 6(-6 + 4r) 65 = -15 + 5r + (-6 * 6 + 4r * 6) 65 = -15 + 5r + (-36 + 24r) Reorder the terms: 65 = -15 + -36 + 5r + 24r Combine like terms: -15 + -36 = -51 65 = -51 + 5r + 24r Combine like terms: 5r + 24r = 29r 65 = -51 + 29r Solving 65 = -51 + 29r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-29r' to each side of the equation. 65 + -29r = -51 + 29r + -29r Combine like terms: 29r + -29r = 0 65 + -29r = -51 + 0 65 + -29r = -51 Add '-65' to each side of the equation. 65 + -65 + -29r = -51 + -65 Combine like terms: 65 + -65 = 0 0 + -29r = -51 + -65 -29r = -51 + -65 Combine like terms: -51 + -65 = -116 -29r = -116 Divide each side by '-29'. r = 4 Simplifying r = 4
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