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Simplifying 6(4t + -3) + 10 = 5(t + -2) + -1(4t + 1) Reorder the terms: 6(-3 + 4t) + 10 = 5(t + -2) + -1(4t + 1) (-3 * 6 + 4t * 6) + 10 = 5(t + -2) + -1(4t + 1) (-18 + 24t) + 10 = 5(t + -2) + -1(4t + 1) Reorder the terms: -18 + 10 + 24t = 5(t + -2) + -1(4t + 1) Combine like terms: -18 + 10 = -8 -8 + 24t = 5(t + -2) + -1(4t + 1) Reorder the terms: -8 + 24t = 5(-2 + t) + -1(4t + 1) -8 + 24t = (-2 * 5 + t * 5) + -1(4t + 1) -8 + 24t = (-10 + 5t) + -1(4t + 1) Reorder the terms: -8 + 24t = -10 + 5t + -1(1 + 4t) -8 + 24t = -10 + 5t + (1 * -1 + 4t * -1) -8 + 24t = -10 + 5t + (-1 + -4t) Reorder the terms: -8 + 24t = -10 + -1 + 5t + -4t Combine like terms: -10 + -1 = -11 -8 + 24t = -11 + 5t + -4t Combine like terms: 5t + -4t = 1t -8 + 24t = -11 + 1t Solving -8 + 24t = -11 + 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. -8 + 24t + -1t = -11 + 1t + -1t Combine like terms: 24t + -1t = 23t -8 + 23t = -11 + 1t + -1t Combine like terms: 1t + -1t = 0 -8 + 23t = -11 + 0 -8 + 23t = -11 Add '8' to each side of the equation. -8 + 8 + 23t = -11 + 8 Combine like terms: -8 + 8 = 0 0 + 23t = -11 + 8 23t = -11 + 8 Combine like terms: -11 + 8 = -3 23t = -3 Divide each side by '23'. t = -0.1304347826 Simplifying t = -0.1304347826
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