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Simplifying 4(t + -3) + -3(9t + -2) = -24(t + 1) + -7 Reorder the terms: 4(-3 + t) + -3(9t + -2) = -24(t + 1) + -7 (-3 * 4 + t * 4) + -3(9t + -2) = -24(t + 1) + -7 (-12 + 4t) + -3(9t + -2) = -24(t + 1) + -7 Reorder the terms: -12 + 4t + -3(-2 + 9t) = -24(t + 1) + -7 -12 + 4t + (-2 * -3 + 9t * -3) = -24(t + 1) + -7 -12 + 4t + (6 + -27t) = -24(t + 1) + -7 Reorder the terms: -12 + 6 + 4t + -27t = -24(t + 1) + -7 Combine like terms: -12 + 6 = -6 -6 + 4t + -27t = -24(t + 1) + -7 Combine like terms: 4t + -27t = -23t -6 + -23t = -24(t + 1) + -7 Reorder the terms: -6 + -23t = -24(1 + t) + -7 -6 + -23t = (1 * -24 + t * -24) + -7 -6 + -23t = (-24 + -24t) + -7 Reorder the terms: -6 + -23t = -24 + -7 + -24t Combine like terms: -24 + -7 = -31 -6 + -23t = -31 + -24t Solving -6 + -23t = -31 + -24t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24t' to each side of the equation. -6 + -23t + 24t = -31 + -24t + 24t Combine like terms: -23t + 24t = 1t -6 + 1t = -31 + -24t + 24t Combine like terms: -24t + 24t = 0 -6 + 1t = -31 + 0 -6 + 1t = -31 Add '6' to each side of the equation. -6 + 6 + 1t = -31 + 6 Combine like terms: -6 + 6 = 0 0 + 1t = -31 + 6 1t = -31 + 6 Combine like terms: -31 + 6 = -25 1t = -25 Divide each side by '1'. t = -25 Simplifying t = -25
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