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Simplifying 10(2r + -3) + -3(r + -4) = 6r + 9 + 12r + -4 Reorder the terms: 10(-3 + 2r) + -3(r + -4) = 6r + 9 + 12r + -4 (-3 * 10 + 2r * 10) + -3(r + -4) = 6r + 9 + 12r + -4 (-30 + 20r) + -3(r + -4) = 6r + 9 + 12r + -4 Reorder the terms: -30 + 20r + -3(-4 + r) = 6r + 9 + 12r + -4 -30 + 20r + (-4 * -3 + r * -3) = 6r + 9 + 12r + -4 -30 + 20r + (12 + -3r) = 6r + 9 + 12r + -4 Reorder the terms: -30 + 12 + 20r + -3r = 6r + 9 + 12r + -4 Combine like terms: -30 + 12 = -18 -18 + 20r + -3r = 6r + 9 + 12r + -4 Combine like terms: 20r + -3r = 17r -18 + 17r = 6r + 9 + 12r + -4 Reorder the terms: -18 + 17r = 9 + -4 + 6r + 12r Combine like terms: 9 + -4 = 5 -18 + 17r = 5 + 6r + 12r Combine like terms: 6r + 12r = 18r -18 + 17r = 5 + 18r Solving -18 + 17r = 5 + 18r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-18r' to each side of the equation. -18 + 17r + -18r = 5 + 18r + -18r Combine like terms: 17r + -18r = -1r -18 + -1r = 5 + 18r + -18r Combine like terms: 18r + -18r = 0 -18 + -1r = 5 + 0 -18 + -1r = 5 Add '18' to each side of the equation. -18 + 18 + -1r = 5 + 18 Combine like terms: -18 + 18 = 0 0 + -1r = 5 + 18 -1r = 5 + 18 Combine like terms: 5 + 18 = 23 -1r = 23 Divide each side by '-1'. r = -23 Simplifying r = -23
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