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Simplifying 10(t + -2) + -6(t + 7) = 3(t + -4) + 60 Reorder the terms: 10(-2 + t) + -6(t + 7) = 3(t + -4) + 60 (-2 * 10 + t * 10) + -6(t + 7) = 3(t + -4) + 60 (-20 + 10t) + -6(t + 7) = 3(t + -4) + 60 Reorder the terms: -20 + 10t + -6(7 + t) = 3(t + -4) + 60 -20 + 10t + (7 * -6 + t * -6) = 3(t + -4) + 60 -20 + 10t + (-42 + -6t) = 3(t + -4) + 60 Reorder the terms: -20 + -42 + 10t + -6t = 3(t + -4) + 60 Combine like terms: -20 + -42 = -62 -62 + 10t + -6t = 3(t + -4) + 60 Combine like terms: 10t + -6t = 4t -62 + 4t = 3(t + -4) + 60 Reorder the terms: -62 + 4t = 3(-4 + t) + 60 -62 + 4t = (-4 * 3 + t * 3) + 60 -62 + 4t = (-12 + 3t) + 60 Reorder the terms: -62 + 4t = -12 + 60 + 3t Combine like terms: -12 + 60 = 48 -62 + 4t = 48 + 3t Solving -62 + 4t = 48 + 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. -62 + 4t + -3t = 48 + 3t + -3t Combine like terms: 4t + -3t = 1t -62 + 1t = 48 + 3t + -3t Combine like terms: 3t + -3t = 0 -62 + 1t = 48 + 0 -62 + 1t = 48 Add '62' to each side of the equation. -62 + 62 + 1t = 48 + 62 Combine like terms: -62 + 62 = 0 0 + 1t = 48 + 62 1t = 48 + 62 Combine like terms: 48 + 62 = 110 1t = 110 Divide each side by '1'. t = 110 Simplifying t = 110
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