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Simplifying 14(2t + -3) + -2(t + 2) = 10(3t + -4) Reorder the terms: 14(-3 + 2t) + -2(t + 2) = 10(3t + -4) (-3 * 14 + 2t * 14) + -2(t + 2) = 10(3t + -4) (-42 + 28t) + -2(t + 2) = 10(3t + -4) Reorder the terms: -42 + 28t + -2(2 + t) = 10(3t + -4) -42 + 28t + (2 * -2 + t * -2) = 10(3t + -4) -42 + 28t + (-4 + -2t) = 10(3t + -4) Reorder the terms: -42 + -4 + 28t + -2t = 10(3t + -4) Combine like terms: -42 + -4 = -46 -46 + 28t + -2t = 10(3t + -4) Combine like terms: 28t + -2t = 26t -46 + 26t = 10(3t + -4) Reorder the terms: -46 + 26t = 10(-4 + 3t) -46 + 26t = (-4 * 10 + 3t * 10) -46 + 26t = (-40 + 30t) Solving -46 + 26t = -40 + 30t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-30t' to each side of the equation. -46 + 26t + -30t = -40 + 30t + -30t Combine like terms: 26t + -30t = -4t -46 + -4t = -40 + 30t + -30t Combine like terms: 30t + -30t = 0 -46 + -4t = -40 + 0 -46 + -4t = -40 Add '46' to each side of the equation. -46 + 46 + -4t = -40 + 46 Combine like terms: -46 + 46 = 0 0 + -4t = -40 + 46 -4t = -40 + 46 Combine like terms: -40 + 46 = 6 -4t = 6 Divide each side by '-4'. t = -1.5 Simplifying t = -1.5
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