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Simplifying 6(t + -7) + 2(5t + 3) = 15(t + -2) + -2 Reorder the terms: 6(-7 + t) + 2(5t + 3) = 15(t + -2) + -2 (-7 * 6 + t * 6) + 2(5t + 3) = 15(t + -2) + -2 (-42 + 6t) + 2(5t + 3) = 15(t + -2) + -2 Reorder the terms: -42 + 6t + 2(3 + 5t) = 15(t + -2) + -2 -42 + 6t + (3 * 2 + 5t * 2) = 15(t + -2) + -2 -42 + 6t + (6 + 10t) = 15(t + -2) + -2 Reorder the terms: -42 + 6 + 6t + 10t = 15(t + -2) + -2 Combine like terms: -42 + 6 = -36 -36 + 6t + 10t = 15(t + -2) + -2 Combine like terms: 6t + 10t = 16t -36 + 16t = 15(t + -2) + -2 Reorder the terms: -36 + 16t = 15(-2 + t) + -2 -36 + 16t = (-2 * 15 + t * 15) + -2 -36 + 16t = (-30 + 15t) + -2 Reorder the terms: -36 + 16t = -30 + -2 + 15t Combine like terms: -30 + -2 = -32 -36 + 16t = -32 + 15t Solving -36 + 16t = -32 + 15t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15t' to each side of the equation. -36 + 16t + -15t = -32 + 15t + -15t Combine like terms: 16t + -15t = 1t -36 + 1t = -32 + 15t + -15t Combine like terms: 15t + -15t = 0 -36 + 1t = -32 + 0 -36 + 1t = -32 Add '36' to each side of the equation. -36 + 36 + 1t = -32 + 36 Combine like terms: -36 + 36 = 0 0 + 1t = -32 + 36 1t = -32 + 36 Combine like terms: -32 + 36 = 4 1t = 4 Divide each side by '1'. t = 4 Simplifying t = 4
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