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Simplifying 2(t + -5) + -3(2t + -7) = 12 + -5(3 + 11) Reorder the terms: 2(-5 + t) + -3(2t + -7) = 12 + -5(3 + 11) (-5 * 2 + t * 2) + -3(2t + -7) = 12 + -5(3 + 11) (-10 + 2t) + -3(2t + -7) = 12 + -5(3 + 11) Reorder the terms: -10 + 2t + -3(-7 + 2t) = 12 + -5(3 + 11) -10 + 2t + (-7 * -3 + 2t * -3) = 12 + -5(3 + 11) -10 + 2t + (21 + -6t) = 12 + -5(3 + 11) Reorder the terms: -10 + 21 + 2t + -6t = 12 + -5(3 + 11) Combine like terms: -10 + 21 = 11 11 + 2t + -6t = 12 + -5(3 + 11) Combine like terms: 2t + -6t = -4t 11 + -4t = 12 + -5(3 + 11) Combine like terms: 3 + 11 = 14 11 + -4t = 12 + -5(14) Multiply -5 * 14 11 + -4t = 12 + -70 Combine like terms: 12 + -70 = -58 11 + -4t = -58 Solving 11 + -4t = -58 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4t = -58 + -11 Combine like terms: 11 + -11 = 0 0 + -4t = -58 + -11 -4t = -58 + -11 Combine like terms: -58 + -11 = -69 -4t = -69 Divide each side by '-4'. t = 17.25 Simplifying t = 17.25
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