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Simplifying 5(4t + -1) + -2(z + 4) = 8(z + 1) Reorder the terms: 5(-1 + 4t) + -2(z + 4) = 8(z + 1) (-1 * 5 + 4t * 5) + -2(z + 4) = 8(z + 1) (-5 + 20t) + -2(z + 4) = 8(z + 1) Reorder the terms: -5 + 20t + -2(4 + z) = 8(z + 1) -5 + 20t + (4 * -2 + z * -2) = 8(z + 1) -5 + 20t + (-8 + -2z) = 8(z + 1) Reorder the terms: -5 + -8 + 20t + -2z = 8(z + 1) Combine like terms: -5 + -8 = -13 -13 + 20t + -2z = 8(z + 1) Reorder the terms: -13 + 20t + -2z = 8(1 + z) -13 + 20t + -2z = (1 * 8 + z * 8) -13 + 20t + -2z = (8 + 8z) Solving -13 + 20t + -2z = 8 + 8z Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 20t + 13 + -2z = 8 + 13 + 8z Reorder the terms: -13 + 13 + 20t + -2z = 8 + 13 + 8z Combine like terms: -13 + 13 = 0 0 + 20t + -2z = 8 + 13 + 8z 20t + -2z = 8 + 13 + 8z Combine like terms: 8 + 13 = 21 20t + -2z = 21 + 8z Add '2z' to each side of the equation. 20t + -2z + 2z = 21 + 8z + 2z Combine like terms: -2z + 2z = 0 20t + 0 = 21 + 8z + 2z 20t = 21 + 8z + 2z Combine like terms: 8z + 2z = 10z 20t = 21 + 10z Divide each side by '20'. t = 1.05 + 0.5z Simplifying t = 1.05 + 0.5z
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