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Simplifying 2(3t + -4) + -6(t + 1) = -1t + 4(t + 10) Reorder the terms: 2(-4 + 3t) + -6(t + 1) = -1t + 4(t + 10) (-4 * 2 + 3t * 2) + -6(t + 1) = -1t + 4(t + 10) (-8 + 6t) + -6(t + 1) = -1t + 4(t + 10) Reorder the terms: -8 + 6t + -6(1 + t) = -1t + 4(t + 10) -8 + 6t + (1 * -6 + t * -6) = -1t + 4(t + 10) -8 + 6t + (-6 + -6t) = -1t + 4(t + 10) Reorder the terms: -8 + -6 + 6t + -6t = -1t + 4(t + 10) Combine like terms: -8 + -6 = -14 -14 + 6t + -6t = -1t + 4(t + 10) Combine like terms: 6t + -6t = 0 -14 + 0 = -1t + 4(t + 10) -14 = -1t + 4(t + 10) Reorder the terms: -14 = -1t + 4(10 + t) -14 = -1t + (10 * 4 + t * 4) -14 = -1t + (40 + 4t) Reorder the terms: -14 = 40 + -1t + 4t Combine like terms: -1t + 4t = 3t -14 = 40 + 3t Solving -14 = 40 + 3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3t' to each side of the equation. -14 + -3t = 40 + 3t + -3t Combine like terms: 3t + -3t = 0 -14 + -3t = 40 + 0 -14 + -3t = 40 Add '14' to each side of the equation. -14 + 14 + -3t = 40 + 14 Combine like terms: -14 + 14 = 0 0 + -3t = 40 + 14 -3t = 40 + 14 Combine like terms: 40 + 14 = 54 -3t = 54 Divide each side by '-3'. t = -18 Simplifying t = -18
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