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Simplifying 4(3t + -2) + 10 = 6(t + -2) + -1(5t + 3) Reorder the terms: 4(-2 + 3t) + 10 = 6(t + -2) + -1(5t + 3) (-2 * 4 + 3t * 4) + 10 = 6(t + -2) + -1(5t + 3) (-8 + 12t) + 10 = 6(t + -2) + -1(5t + 3) Reorder the terms: -8 + 10 + 12t = 6(t + -2) + -1(5t + 3) Combine like terms: -8 + 10 = 2 2 + 12t = 6(t + -2) + -1(5t + 3) Reorder the terms: 2 + 12t = 6(-2 + t) + -1(5t + 3) 2 + 12t = (-2 * 6 + t * 6) + -1(5t + 3) 2 + 12t = (-12 + 6t) + -1(5t + 3) Reorder the terms: 2 + 12t = -12 + 6t + -1(3 + 5t) 2 + 12t = -12 + 6t + (3 * -1 + 5t * -1) 2 + 12t = -12 + 6t + (-3 + -5t) Reorder the terms: 2 + 12t = -12 + -3 + 6t + -5t Combine like terms: -12 + -3 = -15 2 + 12t = -15 + 6t + -5t Combine like terms: 6t + -5t = 1t 2 + 12t = -15 + 1t Solving 2 + 12t = -15 + 1t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1t' to each side of the equation. 2 + 12t + -1t = -15 + 1t + -1t Combine like terms: 12t + -1t = 11t 2 + 11t = -15 + 1t + -1t Combine like terms: 1t + -1t = 0 2 + 11t = -15 + 0 2 + 11t = -15 Add '-2' to each side of the equation. 2 + -2 + 11t = -15 + -2 Combine like terms: 2 + -2 = 0 0 + 11t = -15 + -2 11t = -15 + -2 Combine like terms: -15 + -2 = -17 11t = -17 Divide each side by '11'. t = -1.545454545 Simplifying t = -1.545454545
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