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Simplifying 6(2t + -3) + 13 = 3(t + -3) + -1(2t + 4) Reorder the terms: 6(-3 + 2t) + 13 = 3(t + -3) + -1(2t + 4) (-3 * 6 + 2t * 6) + 13 = 3(t + -3) + -1(2t + 4) (-18 + 12t) + 13 = 3(t + -3) + -1(2t + 4) Reorder the terms: -18 + 13 + 12t = 3(t + -3) + -1(2t + 4) Combine like terms: -18 + 13 = -5 -5 + 12t = 3(t + -3) + -1(2t + 4) Reorder the terms: -5 + 12t = 3(-3 + t) + -1(2t + 4) -5 + 12t = (-3 * 3 + t * 3) + -1(2t + 4) -5 + 12t = (-9 + 3t) + -1(2t + 4) Reorder the terms: -5 + 12t = -9 + 3t + -1(4 + 2t) -5 + 12t = -9 + 3t + (4 * -1 + 2t * -1) -5 + 12t = -9 + 3t + (-4 + -2t) Reorder the terms: -5 + 12t = -9 + -4 + 3t + -2t Combine like terms: -9 + -4 = -13 -5 + 12t = -13 + 3t + -2t Combine like terms: 3t + -2t = 1t -5 + 12t = -13 + 1t Solving -5 + 12t = -13 + 1t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1t' to each side of the equation. -5 + 12t + -1t = -13 + 1t + -1t Combine like terms: 12t + -1t = 11t -5 + 11t = -13 + 1t + -1t Combine like terms: 1t + -1t = 0 -5 + 11t = -13 + 0 -5 + 11t = -13 Add '5' to each side of the equation. -5 + 5 + 11t = -13 + 5 Combine like terms: -5 + 5 = 0 0 + 11t = -13 + 5 11t = -13 + 5 Combine like terms: -13 + 5 = -8 11t = -8 Divide each side by '11'. t = -0.7272727273 Simplifying t = -0.7272727273
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