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Simplifying 3(2R + -7) + 4(5 + -2R) = 5(R + -2) + -54 Reorder the terms: 3(-7 + 2R) + 4(5 + -2R) = 5(R + -2) + -54 (-7 * 3 + 2R * 3) + 4(5 + -2R) = 5(R + -2) + -54 (-21 + 6R) + 4(5 + -2R) = 5(R + -2) + -54 -21 + 6R + (5 * 4 + -2R * 4) = 5(R + -2) + -54 -21 + 6R + (20 + -8R) = 5(R + -2) + -54 Reorder the terms: -21 + 20 + 6R + -8R = 5(R + -2) + -54 Combine like terms: -21 + 20 = -1 -1 + 6R + -8R = 5(R + -2) + -54 Combine like terms: 6R + -8R = -2R -1 + -2R = 5(R + -2) + -54 Reorder the terms: -1 + -2R = 5(-2 + R) + -54 -1 + -2R = (-2 * 5 + R * 5) + -54 -1 + -2R = (-10 + 5R) + -54 Reorder the terms: -1 + -2R = -10 + -54 + 5R Combine like terms: -10 + -54 = -64 -1 + -2R = -64 + 5R Solving -1 + -2R = -64 + 5R Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-5R' to each side of the equation. -1 + -2R + -5R = -64 + 5R + -5R Combine like terms: -2R + -5R = -7R -1 + -7R = -64 + 5R + -5R Combine like terms: 5R + -5R = 0 -1 + -7R = -64 + 0 -1 + -7R = -64 Add '1' to each side of the equation. -1 + 1 + -7R = -64 + 1 Combine like terms: -1 + 1 = 0 0 + -7R = -64 + 1 -7R = -64 + 1 Combine like terms: -64 + 1 = -63 -7R = -63 Divide each side by '-7'. R = 9 Simplifying R = 9
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