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Simplifying 2(3r + -4) + -6(t + 1) = -1t + 4(t + 10) Reorder the terms: 2(-4 + 3r) + -6(t + 1) = -1t + 4(t + 10) (-4 * 2 + 3r * 2) + -6(t + 1) = -1t + 4(t + 10) (-8 + 6r) + -6(t + 1) = -1t + 4(t + 10) Reorder the terms: -8 + 6r + -6(1 + t) = -1t + 4(t + 10) -8 + 6r + (1 * -6 + t * -6) = -1t + 4(t + 10) -8 + 6r + (-6 + -6t) = -1t + 4(t + 10) Reorder the terms: -8 + -6 + 6r + -6t = -1t + 4(t + 10) Combine like terms: -8 + -6 = -14 -14 + 6r + -6t = -1t + 4(t + 10) Reorder the terms: -14 + 6r + -6t = -1t + 4(10 + t) -14 + 6r + -6t = -1t + (10 * 4 + t * 4) -14 + 6r + -6t = -1t + (40 + 4t) Reorder the terms: -14 + 6r + -6t = 40 + -1t + 4t Combine like terms: -1t + 4t = 3t -14 + 6r + -6t = 40 + 3t Solving -14 + 6r + -6t = 40 + 3t Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 6r + 14 + -6t = 40 + 14 + 3t Reorder the terms: -14 + 14 + 6r + -6t = 40 + 14 + 3t Combine like terms: -14 + 14 = 0 0 + 6r + -6t = 40 + 14 + 3t 6r + -6t = 40 + 14 + 3t Combine like terms: 40 + 14 = 54 6r + -6t = 54 + 3t Add '6t' to each side of the equation. 6r + -6t + 6t = 54 + 3t + 6t Combine like terms: -6t + 6t = 0 6r + 0 = 54 + 3t + 6t 6r = 54 + 3t + 6t Combine like terms: 3t + 6t = 9t 6r = 54 + 9t Divide each side by '6'. r = 9 + 1.5t Simplifying r = 9 + 1.5t
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