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Simplifying 4(t + -12) + 2(t + 6) = -3(t + 5) + -3 Reorder the terms: 4(-12 + t) + 2(t + 6) = -3(t + 5) + -3 (-12 * 4 + t * 4) + 2(t + 6) = -3(t + 5) + -3 (-48 + 4t) + 2(t + 6) = -3(t + 5) + -3 Reorder the terms: -48 + 4t + 2(6 + t) = -3(t + 5) + -3 -48 + 4t + (6 * 2 + t * 2) = -3(t + 5) + -3 -48 + 4t + (12 + 2t) = -3(t + 5) + -3 Reorder the terms: -48 + 12 + 4t + 2t = -3(t + 5) + -3 Combine like terms: -48 + 12 = -36 -36 + 4t + 2t = -3(t + 5) + -3 Combine like terms: 4t + 2t = 6t -36 + 6t = -3(t + 5) + -3 Reorder the terms: -36 + 6t = -3(5 + t) + -3 -36 + 6t = (5 * -3 + t * -3) + -3 -36 + 6t = (-15 + -3t) + -3 Reorder the terms: -36 + 6t = -15 + -3 + -3t Combine like terms: -15 + -3 = -18 -36 + 6t = -18 + -3t Solving -36 + 6t = -18 + -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. -36 + 6t + 3t = -18 + -3t + 3t Combine like terms: 6t + 3t = 9t -36 + 9t = -18 + -3t + 3t Combine like terms: -3t + 3t = 0 -36 + 9t = -18 + 0 -36 + 9t = -18 Add '36' to each side of the equation. -36 + 36 + 9t = -18 + 36 Combine like terms: -36 + 36 = 0 0 + 9t = -18 + 36 9t = -18 + 36 Combine like terms: -18 + 36 = 18 9t = 18 Divide each side by '9'. t = 2 Simplifying t = 2
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