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Simplifying 2(3t + 1) + -1(5t + -4) = 11 + 7(t + -5) Reorder the terms: 2(1 + 3t) + -1(5t + -4) = 11 + 7(t + -5) (1 * 2 + 3t * 2) + -1(5t + -4) = 11 + 7(t + -5) (2 + 6t) + -1(5t + -4) = 11 + 7(t + -5) Reorder the terms: 2 + 6t + -1(-4 + 5t) = 11 + 7(t + -5) 2 + 6t + (-4 * -1 + 5t * -1) = 11 + 7(t + -5) 2 + 6t + (4 + -5t) = 11 + 7(t + -5) Reorder the terms: 2 + 4 + 6t + -5t = 11 + 7(t + -5) Combine like terms: 2 + 4 = 6 6 + 6t + -5t = 11 + 7(t + -5) Combine like terms: 6t + -5t = 1t 6 + 1t = 11 + 7(t + -5) Reorder the terms: 6 + 1t = 11 + 7(-5 + t) 6 + 1t = 11 + (-5 * 7 + t * 7) 6 + 1t = 11 + (-35 + 7t) Combine like terms: 11 + -35 = -24 6 + 1t = -24 + 7t Solving 6 + 1t = -24 + 7t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7t' to each side of the equation. 6 + 1t + -7t = -24 + 7t + -7t Combine like terms: 1t + -7t = -6t 6 + -6t = -24 + 7t + -7t Combine like terms: 7t + -7t = 0 6 + -6t = -24 + 0 6 + -6t = -24 Add '-6' to each side of the equation. 6 + -6 + -6t = -24 + -6 Combine like terms: 6 + -6 = 0 0 + -6t = -24 + -6 -6t = -24 + -6 Combine like terms: -24 + -6 = -30 -6t = -30 Divide each side by '-6'. t = 5 Simplifying t = 5
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