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Simplifying 7(t + -8) + -5(4t + -9) = -14(t + -10 + -2) Reorder the terms: 7(-8 + t) + -5(4t + -9) = -14(t + -10 + -2) (-8 * 7 + t * 7) + -5(4t + -9) = -14(t + -10 + -2) (-56 + 7t) + -5(4t + -9) = -14(t + -10 + -2) Reorder the terms: -56 + 7t + -5(-9 + 4t) = -14(t + -10 + -2) -56 + 7t + (-9 * -5 + 4t * -5) = -14(t + -10 + -2) -56 + 7t + (45 + -20t) = -14(t + -10 + -2) Reorder the terms: -56 + 45 + 7t + -20t = -14(t + -10 + -2) Combine like terms: -56 + 45 = -11 -11 + 7t + -20t = -14(t + -10 + -2) Combine like terms: 7t + -20t = -13t -11 + -13t = -14(t + -10 + -2) Reorder the terms: -11 + -13t = -14(-10 + -2 + t) Combine like terms: -10 + -2 = -12 -11 + -13t = -14(-12 + t) -11 + -13t = (-12 * -14 + t * -14) -11 + -13t = (168 + -14t) Solving -11 + -13t = 168 + -14t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14t' to each side of the equation. -11 + -13t + 14t = 168 + -14t + 14t Combine like terms: -13t + 14t = 1t -11 + 1t = 168 + -14t + 14t Combine like terms: -14t + 14t = 0 -11 + 1t = 168 + 0 -11 + 1t = 168 Add '11' to each side of the equation. -11 + 11 + 1t = 168 + 11 Combine like terms: -11 + 11 = 0 0 + 1t = 168 + 11 1t = 168 + 11 Combine like terms: 168 + 11 = 179 1t = 179 Divide each side by '1'. t = 179 Simplifying t = 179
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