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Simplifying 8(t + 2) + (-3)(t * 4) = 6(t + -7) + 8 Reorder the terms: 8(2 + t) + (-3)(t * 4) = 6(t + -7) + 8 (2 * 8 + t * 8) + (-3)(t * 4) = 6(t + -7) + 8 (16 + 8t) + (-3)(t * 4) = 6(t + -7) + 8 Reorder the terms for easier multiplication: 16 + 8t + -3(4t) = 6(t + -7) + 8 Remove parenthesis around (4t) 16 + 8t + -3 * 4t = 6(t + -7) + 8 Multiply -3 * 4 16 + 8t + -12t = 6(t + -7) + 8 Combine like terms: 8t + -12t = -4t 16 + -4t = 6(t + -7) + 8 Reorder the terms: 16 + -4t = 6(-7 + t) + 8 16 + -4t = (-7 * 6 + t * 6) + 8 16 + -4t = (-42 + 6t) + 8 Reorder the terms: 16 + -4t = -42 + 8 + 6t Combine like terms: -42 + 8 = -34 16 + -4t = -34 + 6t Solving 16 + -4t = -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. 16 + -4t + -6t = -34 + 6t + -6t Combine like terms: -4t + -6t = -10t 16 + -10t = -34 + 6t + -6t Combine like terms: 6t + -6t = 0 16 + -10t = -34 + 0 16 + -10t = -34 Add '-16' to each side of the equation. 16 + -16 + -10t = -34 + -16 Combine like terms: 16 + -16 = 0 0 + -10t = -34 + -16 -10t = -34 + -16 Combine like terms: -34 + -16 = -50 -10t = -50 Divide each side by '-10'. t = 5 Simplifying t = 5
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