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Simplifying 5(t + -7) + -2(2t + -7) = 7 + -8(3t + 5) Reorder the terms: 5(-7 + t) + -2(2t + -7) = 7 + -8(3t + 5) (-7 * 5 + t * 5) + -2(2t + -7) = 7 + -8(3t + 5) (-35 + 5t) + -2(2t + -7) = 7 + -8(3t + 5) Reorder the terms: -35 + 5t + -2(-7 + 2t) = 7 + -8(3t + 5) -35 + 5t + (-7 * -2 + 2t * -2) = 7 + -8(3t + 5) -35 + 5t + (14 + -4t) = 7 + -8(3t + 5) Reorder the terms: -35 + 14 + 5t + -4t = 7 + -8(3t + 5) Combine like terms: -35 + 14 = -21 -21 + 5t + -4t = 7 + -8(3t + 5) Combine like terms: 5t + -4t = 1t -21 + 1t = 7 + -8(3t + 5) Reorder the terms: -21 + 1t = 7 + -8(5 + 3t) -21 + 1t = 7 + (5 * -8 + 3t * -8) -21 + 1t = 7 + (-40 + -24t) Combine like terms: 7 + -40 = -33 -21 + 1t = -33 + -24t Solving -21 + 1t = -33 + -24t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24t' to each side of the equation. -21 + 1t + 24t = -33 + -24t + 24t Combine like terms: 1t + 24t = 25t -21 + 25t = -33 + -24t + 24t Combine like terms: -24t + 24t = 0 -21 + 25t = -33 + 0 -21 + 25t = -33 Add '21' to each side of the equation. -21 + 21 + 25t = -33 + 21 Combine like terms: -21 + 21 = 0 0 + 25t = -33 + 21 25t = -33 + 21 Combine like terms: -33 + 21 = -12 25t = -12 Divide each side by '25'. t = -0.48 Simplifying t = -0.48
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