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Simplifying 4(2r + -3) + -2(r + -4) = 3(r + -3) + -1 Reorder the terms: 4(-3 + 2r) + -2(r + -4) = 3(r + -3) + -1 (-3 * 4 + 2r * 4) + -2(r + -4) = 3(r + -3) + -1 (-12 + 8r) + -2(r + -4) = 3(r + -3) + -1 Reorder the terms: -12 + 8r + -2(-4 + r) = 3(r + -3) + -1 -12 + 8r + (-4 * -2 + r * -2) = 3(r + -3) + -1 -12 + 8r + (8 + -2r) = 3(r + -3) + -1 Reorder the terms: -12 + 8 + 8r + -2r = 3(r + -3) + -1 Combine like terms: -12 + 8 = -4 -4 + 8r + -2r = 3(r + -3) + -1 Combine like terms: 8r + -2r = 6r -4 + 6r = 3(r + -3) + -1 Reorder the terms: -4 + 6r = 3(-3 + r) + -1 -4 + 6r = (-3 * 3 + r * 3) + -1 -4 + 6r = (-9 + 3r) + -1 Reorder the terms: -4 + 6r = -9 + -1 + 3r Combine like terms: -9 + -1 = -10 -4 + 6r = -10 + 3r Solving -4 + 6r = -10 + 3r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3r' to each side of the equation. -4 + 6r + -3r = -10 + 3r + -3r Combine like terms: 6r + -3r = 3r -4 + 3r = -10 + 3r + -3r Combine like terms: 3r + -3r = 0 -4 + 3r = -10 + 0 -4 + 3r = -10 Add '4' to each side of the equation. -4 + 4 + 3r = -10 + 4 Combine like terms: -4 + 4 = 0 0 + 3r = -10 + 4 3r = -10 + 4 Combine like terms: -10 + 4 = -6 3r = -6 Divide each side by '3'. r = -2 Simplifying r = -2
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