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Simplifying 7(6y + -8) + -1(1 + -4y) = 7 + -4(y + -9) Reorder the terms: 7(-8 + 6y) + -1(1 + -4y) = 7 + -4(y + -9) (-8 * 7 + 6y * 7) + -1(1 + -4y) = 7 + -4(y + -9) (-56 + 42y) + -1(1 + -4y) = 7 + -4(y + -9) -56 + 42y + (1 * -1 + -4y * -1) = 7 + -4(y + -9) -56 + 42y + (-1 + 4y) = 7 + -4(y + -9) Reorder the terms: -56 + -1 + 42y + 4y = 7 + -4(y + -9) Combine like terms: -56 + -1 = -57 -57 + 42y + 4y = 7 + -4(y + -9) Combine like terms: 42y + 4y = 46y -57 + 46y = 7 + -4(y + -9) Reorder the terms: -57 + 46y = 7 + -4(-9 + y) -57 + 46y = 7 + (-9 * -4 + y * -4) -57 + 46y = 7 + (36 + -4y) Combine like terms: 7 + 36 = 43 -57 + 46y = 43 + -4y Solving -57 + 46y = 43 + -4y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4y' to each side of the equation. -57 + 46y + 4y = 43 + -4y + 4y Combine like terms: 46y + 4y = 50y -57 + 50y = 43 + -4y + 4y Combine like terms: -4y + 4y = 0 -57 + 50y = 43 + 0 -57 + 50y = 43 Add '57' to each side of the equation. -57 + 57 + 50y = 43 + 57 Combine like terms: -57 + 57 = 0 0 + 50y = 43 + 57 50y = 43 + 57 Combine like terms: 43 + 57 = 100 50y = 100 Divide each side by '50'. y = 2 Simplifying y = 2
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