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Simplifying 8(t + -12) + -3(t + -4) = 6(t + -7) + -8 Reorder the terms: 8(-12 + t) + -3(t + -4) = 6(t + -7) + -8 (-12 * 8 + t * 8) + -3(t + -4) = 6(t + -7) + -8 (-96 + 8t) + -3(t + -4) = 6(t + -7) + -8 Reorder the terms: -96 + 8t + -3(-4 + t) = 6(t + -7) + -8 -96 + 8t + (-4 * -3 + t * -3) = 6(t + -7) + -8 -96 + 8t + (12 + -3t) = 6(t + -7) + -8 Reorder the terms: -96 + 12 + 8t + -3t = 6(t + -7) + -8 Combine like terms: -96 + 12 = -84 -84 + 8t + -3t = 6(t + -7) + -8 Combine like terms: 8t + -3t = 5t -84 + 5t = 6(t + -7) + -8 Reorder the terms: -84 + 5t = 6(-7 + t) + -8 -84 + 5t = (-7 * 6 + t * 6) + -8 -84 + 5t = (-42 + 6t) + -8 Reorder the terms: -84 + 5t = -42 + -8 + 6t Combine like terms: -42 + -8 = -50 -84 + 5t = -50 + 6t Solving -84 + 5t = -50 + 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. -84 + 5t + -6t = -50 + 6t + -6t Combine like terms: 5t + -6t = -1t -84 + -1t = -50 + 6t + -6t Combine like terms: 6t + -6t = 0 -84 + -1t = -50 + 0 -84 + -1t = -50 Add '84' to each side of the equation. -84 + 84 + -1t = -50 + 84 Combine like terms: -84 + 84 = 0 0 + -1t = -50 + 84 -1t = -50 + 84 Combine like terms: -50 + 84 = 34 -1t = 34 Divide each side by '-1'. t = -34 Simplifying t = -34
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