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Simplifying 8(t + 2) + -3(t + -4) = 6(t + -7) + 5t Reorder the terms: 8(2 + t) + -3(t + -4) = 6(t + -7) + 5t (2 * 8 + t * 8) + -3(t + -4) = 6(t + -7) + 5t (16 + 8t) + -3(t + -4) = 6(t + -7) + 5t Reorder the terms: 16 + 8t + -3(-4 + t) = 6(t + -7) + 5t 16 + 8t + (-4 * -3 + t * -3) = 6(t + -7) + 5t 16 + 8t + (12 + -3t) = 6(t + -7) + 5t Reorder the terms: 16 + 12 + 8t + -3t = 6(t + -7) + 5t Combine like terms: 16 + 12 = 28 28 + 8t + -3t = 6(t + -7) + 5t Combine like terms: 8t + -3t = 5t 28 + 5t = 6(t + -7) + 5t Reorder the terms: 28 + 5t = 6(-7 + t) + 5t 28 + 5t = (-7 * 6 + t * 6) + 5t 28 + 5t = (-42 + 6t) + 5t Combine like terms: 6t + 5t = 11t 28 + 5t = -42 + 11t Solving 28 + 5t = -42 + 11t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11t' to each side of the equation. 28 + 5t + -11t = -42 + 11t + -11t Combine like terms: 5t + -11t = -6t 28 + -6t = -42 + 11t + -11t Combine like terms: 11t + -11t = 0 28 + -6t = -42 + 0 28 + -6t = -42 Add '-28' to each side of the equation. 28 + -28 + -6t = -42 + -28 Combine like terms: 28 + -28 = 0 0 + -6t = -42 + -28 -6t = -42 + -28 Combine like terms: -42 + -28 = -70 -6t = -70 Divide each side by '-6'. t = 11.66666667 Simplifying t = 11.66666667
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