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Simplifying 5 + 5(t + -4) = 2(t + -3) + 3 Reorder the terms: 5 + 5(-4 + t) = 2(t + -3) + 3 5 + (-4 * 5 + t * 5) = 2(t + -3) + 3 5 + (-20 + 5t) = 2(t + -3) + 3 Combine like terms: 5 + -20 = -15 -15 + 5t = 2(t + -3) + 3 Reorder the terms: -15 + 5t = 2(-3 + t) + 3 -15 + 5t = (-3 * 2 + t * 2) + 3 -15 + 5t = (-6 + 2t) + 3 Reorder the terms: -15 + 5t = -6 + 3 + 2t Combine like terms: -6 + 3 = -3 -15 + 5t = -3 + 2t Solving -15 + 5t = -3 + 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. -15 + 5t + -2t = -3 + 2t + -2t Combine like terms: 5t + -2t = 3t -15 + 3t = -3 + 2t + -2t Combine like terms: 2t + -2t = 0 -15 + 3t = -3 + 0 -15 + 3t = -3 Add '15' to each side of the equation. -15 + 15 + 3t = -3 + 15 Combine like terms: -15 + 15 = 0 0 + 3t = -3 + 15 3t = -3 + 15 Combine like terms: -3 + 15 = 12 3t = 12 Divide each side by '3'. t = 4 Simplifying t = 4
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