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Simplifying 3(2t + -5) + -1(2t + -2) = -54 + -1(5t + 4) Reorder the terms: 3(-5 + 2t) + -1(2t + -2) = -54 + -1(5t + 4) (-5 * 3 + 2t * 3) + -1(2t + -2) = -54 + -1(5t + 4) (-15 + 6t) + -1(2t + -2) = -54 + -1(5t + 4) Reorder the terms: -15 + 6t + -1(-2 + 2t) = -54 + -1(5t + 4) -15 + 6t + (-2 * -1 + 2t * -1) = -54 + -1(5t + 4) -15 + 6t + (2 + -2t) = -54 + -1(5t + 4) Reorder the terms: -15 + 2 + 6t + -2t = -54 + -1(5t + 4) Combine like terms: -15 + 2 = -13 -13 + 6t + -2t = -54 + -1(5t + 4) Combine like terms: 6t + -2t = 4t -13 + 4t = -54 + -1(5t + 4) Reorder the terms: -13 + 4t = -54 + -1(4 + 5t) -13 + 4t = -54 + (4 * -1 + 5t * -1) -13 + 4t = -54 + (-4 + -5t) Combine like terms: -54 + -4 = -58 -13 + 4t = -58 + -5t Solving -13 + 4t = -58 + -5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5t' to each side of the equation. -13 + 4t + 5t = -58 + -5t + 5t Combine like terms: 4t + 5t = 9t -13 + 9t = -58 + -5t + 5t Combine like terms: -5t + 5t = 0 -13 + 9t = -58 + 0 -13 + 9t = -58 Add '13' to each side of the equation. -13 + 13 + 9t = -58 + 13 Combine like terms: -13 + 13 = 0 0 + 9t = -58 + 13 9t = -58 + 13 Combine like terms: -58 + 13 = -45 9t = -45 Divide each side by '9'. t = -5 Simplifying t = -5
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