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Simplifying 10r + -3(r + 4) = 4(3r + -4) + -31 Reorder the terms: 10r + -3(4 + r) = 4(3r + -4) + -31 10r + (4 * -3 + r * -3) = 4(3r + -4) + -31 10r + (-12 + -3r) = 4(3r + -4) + -31 Reorder the terms: -12 + 10r + -3r = 4(3r + -4) + -31 Combine like terms: 10r + -3r = 7r -12 + 7r = 4(3r + -4) + -31 Reorder the terms: -12 + 7r = 4(-4 + 3r) + -31 -12 + 7r = (-4 * 4 + 3r * 4) + -31 -12 + 7r = (-16 + 12r) + -31 Reorder the terms: -12 + 7r = -16 + -31 + 12r Combine like terms: -16 + -31 = -47 -12 + 7r = -47 + 12r Solving -12 + 7r = -47 + 12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. -12 + 7r + -12r = -47 + 12r + -12r Combine like terms: 7r + -12r = -5r -12 + -5r = -47 + 12r + -12r Combine like terms: 12r + -12r = 0 -12 + -5r = -47 + 0 -12 + -5r = -47 Add '12' to each side of the equation. -12 + 12 + -5r = -47 + 12 Combine like terms: -12 + 12 = 0 0 + -5r = -47 + 12 -5r = -47 + 12 Combine like terms: -47 + 12 = -35 -5r = -35 Divide each side by '-5'. r = 7 Simplifying r = 7
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