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Simplifying -10(y + 1) + 5(3y + -7) = 4(y + -3) + 13 Reorder the terms: -10(1 + y) + 5(3y + -7) = 4(y + -3) + 13 (1 * -10 + y * -10) + 5(3y + -7) = 4(y + -3) + 13 (-10 + -10y) + 5(3y + -7) = 4(y + -3) + 13 Reorder the terms: -10 + -10y + 5(-7 + 3y) = 4(y + -3) + 13 -10 + -10y + (-7 * 5 + 3y * 5) = 4(y + -3) + 13 -10 + -10y + (-35 + 15y) = 4(y + -3) + 13 Reorder the terms: -10 + -35 + -10y + 15y = 4(y + -3) + 13 Combine like terms: -10 + -35 = -45 -45 + -10y + 15y = 4(y + -3) + 13 Combine like terms: -10y + 15y = 5y -45 + 5y = 4(y + -3) + 13 Reorder the terms: -45 + 5y = 4(-3 + y) + 13 -45 + 5y = (-3 * 4 + y * 4) + 13 -45 + 5y = (-12 + 4y) + 13 Reorder the terms: -45 + 5y = -12 + 13 + 4y Combine like terms: -12 + 13 = 1 -45 + 5y = 1 + 4y Solving -45 + 5y = 1 + 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. -45 + 5y + -4y = 1 + 4y + -4y Combine like terms: 5y + -4y = 1y -45 + 1y = 1 + 4y + -4y Combine like terms: 4y + -4y = 0 -45 + 1y = 1 + 0 -45 + 1y = 1 Add '45' to each side of the equation. -45 + 45 + 1y = 1 + 45 Combine like terms: -45 + 45 = 0 0 + 1y = 1 + 45 1y = 1 + 45 Combine like terms: 1 + 45 = 46 1y = 46 Divide each side by '1'. y = 46 Simplifying y = 46
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