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Simplifying 8(t + -7) + -3(t + -4) = 6(t + -7) + 8 Reorder the terms: 8(-7 + t) + -3(t + -4) = 6(t + -7) + 8 (-7 * 8 + t * 8) + -3(t + -4) = 6(t + -7) + 8 (-56 + 8t) + -3(t + -4) = 6(t + -7) + 8 Reorder the terms: -56 + 8t + -3(-4 + t) = 6(t + -7) + 8 -56 + 8t + (-4 * -3 + t * -3) = 6(t + -7) + 8 -56 + 8t + (12 + -3t) = 6(t + -7) + 8 Reorder the terms: -56 + 12 + 8t + -3t = 6(t + -7) + 8 Combine like terms: -56 + 12 = -44 -44 + 8t + -3t = 6(t + -7) + 8 Combine like terms: 8t + -3t = 5t -44 + 5t = 6(t + -7) + 8 Reorder the terms: -44 + 5t = 6(-7 + t) + 8 -44 + 5t = (-7 * 6 + t * 6) + 8 -44 + 5t = (-42 + 6t) + 8 Reorder the terms: -44 + 5t = -42 + 8 + 6t Combine like terms: -42 + 8 = -34 -44 + 5t = -34 + 6t Solving -44 + 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. -44 + 5t + -6t = -34 + 6t + -6t Combine like terms: 5t + -6t = -1t -44 + -1t = -34 + 6t + -6t Combine like terms: 6t + -6t = 0 -44 + -1t = -34 + 0 -44 + -1t = -34 Add '44' to each side of the equation. -44 + 44 + -1t = -34 + 44 Combine like terms: -44 + 44 = 0 0 + -1t = -34 + 44 -1t = -34 + 44 Combine like terms: -34 + 44 = 10 -1t = 10 Divide each side by '-1'. t = -10 Simplifying t = -10
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