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Simplifying 4(t + -1) + 4(3t + -6) = 15(t + -3) + 4 Reorder the terms: 4(-1 + t) + 4(3t + -6) = 15(t + -3) + 4 (-1 * 4 + t * 4) + 4(3t + -6) = 15(t + -3) + 4 (-4 + 4t) + 4(3t + -6) = 15(t + -3) + 4 Reorder the terms: -4 + 4t + 4(-6 + 3t) = 15(t + -3) + 4 -4 + 4t + (-6 * 4 + 3t * 4) = 15(t + -3) + 4 -4 + 4t + (-24 + 12t) = 15(t + -3) + 4 Reorder the terms: -4 + -24 + 4t + 12t = 15(t + -3) + 4 Combine like terms: -4 + -24 = -28 -28 + 4t + 12t = 15(t + -3) + 4 Combine like terms: 4t + 12t = 16t -28 + 16t = 15(t + -3) + 4 Reorder the terms: -28 + 16t = 15(-3 + t) + 4 -28 + 16t = (-3 * 15 + t * 15) + 4 -28 + 16t = (-45 + 15t) + 4 Reorder the terms: -28 + 16t = -45 + 4 + 15t Combine like terms: -45 + 4 = -41 -28 + 16t = -41 + 15t Solving -28 + 16t = -41 + 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. -28 + 16t + -15t = -41 + 15t + -15t Combine like terms: 16t + -15t = 1t -28 + 1t = -41 + 15t + -15t Combine like terms: 15t + -15t = 0 -28 + 1t = -41 + 0 -28 + 1t = -41 Add '28' to each side of the equation. -28 + 28 + 1t = -41 + 28 Combine like terms: -28 + 28 = 0 0 + 1t = -41 + 28 1t = -41 + 28 Combine like terms: -41 + 28 = -13 1t = -13 Divide each side by '1'. t = -13 Simplifying t = -13
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