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Simplifying 7(-4t + 3 + -2) = 6(5 + 2t + -7) Reorder the terms: 7(3 + -2 + -4t) = 6(5 + 2t + -7) Combine like terms: 3 + -2 = 1 7(1 + -4t) = 6(5 + 2t + -7) (1 * 7 + -4t * 7) = 6(5 + 2t + -7) (7 + -28t) = 6(5 + 2t + -7) Reorder the terms: 7 + -28t = 6(5 + -7 + 2t) Combine like terms: 5 + -7 = -2 7 + -28t = 6(-2 + 2t) 7 + -28t = (-2 * 6 + 2t * 6) 7 + -28t = (-12 + 12t) Solving 7 + -28t = -12 + 12t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12t' to each side of the equation. 7 + -28t + -12t = -12 + 12t + -12t Combine like terms: -28t + -12t = -40t 7 + -40t = -12 + 12t + -12t Combine like terms: 12t + -12t = 0 7 + -40t = -12 + 0 7 + -40t = -12 Add '-7' to each side of the equation. 7 + -7 + -40t = -12 + -7 Combine like terms: 7 + -7 = 0 0 + -40t = -12 + -7 -40t = -12 + -7 Combine like terms: -12 + -7 = -19 -40t = -19 Divide each side by '-40'. t = 0.475 Simplifying t = 0.475
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