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Simplifying 2(t + -6) + 4(t + -12) = -2(t + -5) + 3 Reorder the terms: 2(-6 + t) + 4(t + -12) = -2(t + -5) + 3 (-6 * 2 + t * 2) + 4(t + -12) = -2(t + -5) + 3 (-12 + 2t) + 4(t + -12) = -2(t + -5) + 3 Reorder the terms: -12 + 2t + 4(-12 + t) = -2(t + -5) + 3 -12 + 2t + (-12 * 4 + t * 4) = -2(t + -5) + 3 -12 + 2t + (-48 + 4t) = -2(t + -5) + 3 Reorder the terms: -12 + -48 + 2t + 4t = -2(t + -5) + 3 Combine like terms: -12 + -48 = -60 -60 + 2t + 4t = -2(t + -5) + 3 Combine like terms: 2t + 4t = 6t -60 + 6t = -2(t + -5) + 3 Reorder the terms: -60 + 6t = -2(-5 + t) + 3 -60 + 6t = (-5 * -2 + t * -2) + 3 -60 + 6t = (10 + -2t) + 3 Reorder the terms: -60 + 6t = 10 + 3 + -2t Combine like terms: 10 + 3 = 13 -60 + 6t = 13 + -2t Solving -60 + 6t = 13 + -2t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2t' to each side of the equation. -60 + 6t + 2t = 13 + -2t + 2t Combine like terms: 6t + 2t = 8t -60 + 8t = 13 + -2t + 2t Combine like terms: -2t + 2t = 0 -60 + 8t = 13 + 0 -60 + 8t = 13 Add '60' to each side of the equation. -60 + 60 + 8t = 13 + 60 Combine like terms: -60 + 60 = 0 0 + 8t = 13 + 60 8t = 13 + 60 Combine like terms: 13 + 60 = 73 8t = 73 Divide each side by '8'. t = 9.125 Simplifying t = 9.125
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