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Simplifying 4(r + -2) + -3(r + -1) = 2(r + 4) Reorder the terms: 4(-2 + r) + -3(r + -1) = 2(r + 4) (-2 * 4 + r * 4) + -3(r + -1) = 2(r + 4) (-8 + 4r) + -3(r + -1) = 2(r + 4) Reorder the terms: -8 + 4r + -3(-1 + r) = 2(r + 4) -8 + 4r + (-1 * -3 + r * -3) = 2(r + 4) -8 + 4r + (3 + -3r) = 2(r + 4) Reorder the terms: -8 + 3 + 4r + -3r = 2(r + 4) Combine like terms: -8 + 3 = -5 -5 + 4r + -3r = 2(r + 4) Combine like terms: 4r + -3r = 1r -5 + 1r = 2(r + 4) Reorder the terms: -5 + 1r = 2(4 + r) -5 + 1r = (4 * 2 + r * 2) -5 + 1r = (8 + 2r) Solving -5 + 1r = 8 + 2r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2r' to each side of the equation. -5 + 1r + -2r = 8 + 2r + -2r Combine like terms: 1r + -2r = -1r -5 + -1r = 8 + 2r + -2r Combine like terms: 2r + -2r = 0 -5 + -1r = 8 + 0 -5 + -1r = 8 Add '5' to each side of the equation. -5 + 5 + -1r = 8 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 8 + 5 -1r = 8 + 5 Combine like terms: 8 + 5 = 13 -1r = 13 Divide each side by '-1'. r = -13 Simplifying r = -13
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