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Simplifying -9(t + 7) + 5(6 + -5t) = -35(t + 2) + 8 Reorder the terms: -9(7 + t) + 5(6 + -5t) = -35(t + 2) + 8 (7 * -9 + t * -9) + 5(6 + -5t) = -35(t + 2) + 8 (-63 + -9t) + 5(6 + -5t) = -35(t + 2) + 8 -63 + -9t + (6 * 5 + -5t * 5) = -35(t + 2) + 8 -63 + -9t + (30 + -25t) = -35(t + 2) + 8 Reorder the terms: -63 + 30 + -9t + -25t = -35(t + 2) + 8 Combine like terms: -63 + 30 = -33 -33 + -9t + -25t = -35(t + 2) + 8 Combine like terms: -9t + -25t = -34t -33 + -34t = -35(t + 2) + 8 Reorder the terms: -33 + -34t = -35(2 + t) + 8 -33 + -34t = (2 * -35 + t * -35) + 8 -33 + -34t = (-70 + -35t) + 8 Reorder the terms: -33 + -34t = -70 + 8 + -35t Combine like terms: -70 + 8 = -62 -33 + -34t = -62 + -35t Solving -33 + -34t = -62 + -35t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35t' to each side of the equation. -33 + -34t + 35t = -62 + -35t + 35t Combine like terms: -34t + 35t = 1t -33 + 1t = -62 + -35t + 35t Combine like terms: -35t + 35t = 0 -33 + 1t = -62 + 0 -33 + 1t = -62 Add '33' to each side of the equation. -33 + 33 + 1t = -62 + 33 Combine like terms: -33 + 33 = 0 0 + 1t = -62 + 33 1t = -62 + 33 Combine like terms: -62 + 33 = -29 1t = -29 Divide each side by '1'. t = -29 Simplifying t = -29
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