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Simplifying 0.5(3t + 2) + -0.25(x + 6) = 0 Reorder the terms: 0.5(2 + 3t) + -0.25(x + 6) = 0 (2 * 0.5 + 3t * 0.5) + -0.25(x + 6) = 0 (1 + 1.5t) + -0.25(x + 6) = 0 Reorder the terms: 1 + 1.5t + -0.25(6 + x) = 0 1 + 1.5t + (6 * -0.25 + x * -0.25) = 0 1 + 1.5t + (-1.5 + -0.25x) = 0 Reorder the terms: 1 + -1.5 + 1.5t + -0.25x = 0 Combine like terms: 1 + -1.5 = -0.5 -0.5 + 1.5t + -0.25x = 0 Solving -0.5 + 1.5t + -0.25x = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 1.5t + 0.5 + -0.25x = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.5t + -0.25x = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.5t + -0.25x = 0 + 0.5 1.5t + -0.25x = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.5t + -0.25x = 0.5 Add '0.25x' to each side of the equation. 1.5t + -0.25x + 0.25x = 0.5 + 0.25x Combine like terms: -0.25x + 0.25x = 0.00 1.5t + 0.00 = 0.5 + 0.25x 1.5t = 0.5 + 0.25x Divide each side by '1.5'. t = 0.3333333333 + 0.1666666667x Simplifying t = 0.3333333333 + 0.1666666667x
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