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Simplifying 3(r + -3) + 8(r + 1) = -4(r + -10) + 4 Reorder the terms: 3(-3 + r) + 8(r + 1) = -4(r + -10) + 4 (-3 * 3 + r * 3) + 8(r + 1) = -4(r + -10) + 4 (-9 + 3r) + 8(r + 1) = -4(r + -10) + 4 Reorder the terms: -9 + 3r + 8(1 + r) = -4(r + -10) + 4 -9 + 3r + (1 * 8 + r * 8) = -4(r + -10) + 4 -9 + 3r + (8 + 8r) = -4(r + -10) + 4 Reorder the terms: -9 + 8 + 3r + 8r = -4(r + -10) + 4 Combine like terms: -9 + 8 = -1 -1 + 3r + 8r = -4(r + -10) + 4 Combine like terms: 3r + 8r = 11r -1 + 11r = -4(r + -10) + 4 Reorder the terms: -1 + 11r = -4(-10 + r) + 4 -1 + 11r = (-10 * -4 + r * -4) + 4 -1 + 11r = (40 + -4r) + 4 Reorder the terms: -1 + 11r = 40 + 4 + -4r Combine like terms: 40 + 4 = 44 -1 + 11r = 44 + -4r Solving -1 + 11r = 44 + -4r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4r' to each side of the equation. -1 + 11r + 4r = 44 + -4r + 4r Combine like terms: 11r + 4r = 15r -1 + 15r = 44 + -4r + 4r Combine like terms: -4r + 4r = 0 -1 + 15r = 44 + 0 -1 + 15r = 44 Add '1' to each side of the equation. -1 + 1 + 15r = 44 + 1 Combine like terms: -1 + 1 = 0 0 + 15r = 44 + 1 15r = 44 + 1 Combine like terms: 44 + 1 = 45 15r = 45 Divide each side by '15'. r = 3 Simplifying r = 3
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