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Simplifying 2(4r + -5) + 6(r + 2) = 8(r + -5) Reorder the terms: 2(-5 + 4r) + 6(r + 2) = 8(r + -5) (-5 * 2 + 4r * 2) + 6(r + 2) = 8(r + -5) (-10 + 8r) + 6(r + 2) = 8(r + -5) Reorder the terms: -10 + 8r + 6(2 + r) = 8(r + -5) -10 + 8r + (2 * 6 + r * 6) = 8(r + -5) -10 + 8r + (12 + 6r) = 8(r + -5) Reorder the terms: -10 + 12 + 8r + 6r = 8(r + -5) Combine like terms: -10 + 12 = 2 2 + 8r + 6r = 8(r + -5) Combine like terms: 8r + 6r = 14r 2 + 14r = 8(r + -5) Reorder the terms: 2 + 14r = 8(-5 + r) 2 + 14r = (-5 * 8 + r * 8) 2 + 14r = (-40 + 8r) Solving 2 + 14r = -40 + 8r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8r' to each side of the equation. 2 + 14r + -8r = -40 + 8r + -8r Combine like terms: 14r + -8r = 6r 2 + 6r = -40 + 8r + -8r Combine like terms: 8r + -8r = 0 2 + 6r = -40 + 0 2 + 6r = -40 Add '-2' to each side of the equation. 2 + -2 + 6r = -40 + -2 Combine like terms: 2 + -2 = 0 0 + 6r = -40 + -2 6r = -40 + -2 Combine like terms: -40 + -2 = -42 6r = -42 Divide each side by '6'. r = -7 Simplifying r = -7
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