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Simplifying 3(4t + 5) + -2(3r + 4) = 7 Reorder the terms: 3(5 + 4t) + -2(3r + 4) = 7 (5 * 3 + 4t * 3) + -2(3r + 4) = 7 (15 + 12t) + -2(3r + 4) = 7 Reorder the terms: 15 + 12t + -2(4 + 3r) = 7 15 + 12t + (4 * -2 + 3r * -2) = 7 15 + 12t + (-8 + -6r) = 7 Reorder the terms: 15 + -8 + -6r + 12t = 7 Combine like terms: 15 + -8 = 7 7 + -6r + 12t = 7 Add '-7' to each side of the equation. 7 + -6r + -7 + 12t = 7 + -7 Reorder the terms: 7 + -7 + -6r + 12t = 7 + -7 Combine like terms: 7 + -7 = 0 0 + -6r + 12t = 7 + -7 -6r + 12t = 7 + -7 Combine like terms: 7 + -7 = 0 -6r + 12t = 0 Solving -6r + 12t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12t' to each side of the equation. -6r + 12t + -12t = 0 + -12t Combine like terms: 12t + -12t = 0 -6r + 0 = 0 + -12t -6r = 0 + -12t Remove the zero: -6r = -12t Divide each side by '-6'. r = 2t Simplifying r = 2t
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