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Simplifying 8(t + 21) + -3(t + -4) = 6(t + -7) + 8 Reorder the terms: 8(21 + t) + -3(t + -4) = 6(t + -7) + 8 (21 * 8 + t * 8) + -3(t + -4) = 6(t + -7) + 8 (168 + 8t) + -3(t + -4) = 6(t + -7) + 8 Reorder the terms: 168 + 8t + -3(-4 + t) = 6(t + -7) + 8 168 + 8t + (-4 * -3 + t * -3) = 6(t + -7) + 8 168 + 8t + (12 + -3t) = 6(t + -7) + 8 Reorder the terms: 168 + 12 + 8t + -3t = 6(t + -7) + 8 Combine like terms: 168 + 12 = 180 180 + 8t + -3t = 6(t + -7) + 8 Combine like terms: 8t + -3t = 5t 180 + 5t = 6(t + -7) + 8 Reorder the terms: 180 + 5t = 6(-7 + t) + 8 180 + 5t = (-7 * 6 + t * 6) + 8 180 + 5t = (-42 + 6t) + 8 Reorder the terms: 180 + 5t = -42 + 8 + 6t Combine like terms: -42 + 8 = -34 180 + 5t = -34 + 6t Solving 180 + 5t = -34 + 6t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6t' to each side of the equation. 180 + 5t + -6t = -34 + 6t + -6t Combine like terms: 5t + -6t = -1t 180 + -1t = -34 + 6t + -6t Combine like terms: 6t + -6t = 0 180 + -1t = -34 + 0 180 + -1t = -34 Add '-180' to each side of the equation. 180 + -180 + -1t = -34 + -180 Combine like terms: 180 + -180 = 0 0 + -1t = -34 + -180 -1t = -34 + -180 Combine like terms: -34 + -180 = -214 -1t = -214 Divide each side by '-1'. t = 214 Simplifying t = 214
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