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Simplifying 5(2r + -7) + 3(r + 4) = 4(r + 1) Reorder the terms: 5(-7 + 2r) + 3(r + 4) = 4(r + 1) (-7 * 5 + 2r * 5) + 3(r + 4) = 4(r + 1) (-35 + 10r) + 3(r + 4) = 4(r + 1) Reorder the terms: -35 + 10r + 3(4 + r) = 4(r + 1) -35 + 10r + (4 * 3 + r * 3) = 4(r + 1) -35 + 10r + (12 + 3r) = 4(r + 1) Reorder the terms: -35 + 12 + 10r + 3r = 4(r + 1) Combine like terms: -35 + 12 = -23 -23 + 10r + 3r = 4(r + 1) Combine like terms: 10r + 3r = 13r -23 + 13r = 4(r + 1) Reorder the terms: -23 + 13r = 4(1 + r) -23 + 13r = (1 * 4 + r * 4) -23 + 13r = (4 + 4r) Solving -23 + 13r = 4 + 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. -23 + 13r + -4r = 4 + 4r + -4r Combine like terms: 13r + -4r = 9r -23 + 9r = 4 + 4r + -4r Combine like terms: 4r + -4r = 0 -23 + 9r = 4 + 0 -23 + 9r = 4 Add '23' to each side of the equation. -23 + 23 + 9r = 4 + 23 Combine like terms: -23 + 23 = 0 0 + 9r = 4 + 23 9r = 4 + 23 Combine like terms: 4 + 23 = 27 9r = 27 Divide each side by '9'. r = 3 Simplifying r = 3
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