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Simplifying 2(y + -5) + 3(y + -2) = 8 + 7(y + -4) Reorder the terms: 2(-5 + y) + 3(y + -2) = 8 + 7(y + -4) (-5 * 2 + y * 2) + 3(y + -2) = 8 + 7(y + -4) (-10 + 2y) + 3(y + -2) = 8 + 7(y + -4) Reorder the terms: -10 + 2y + 3(-2 + y) = 8 + 7(y + -4) -10 + 2y + (-2 * 3 + y * 3) = 8 + 7(y + -4) -10 + 2y + (-6 + 3y) = 8 + 7(y + -4) Reorder the terms: -10 + -6 + 2y + 3y = 8 + 7(y + -4) Combine like terms: -10 + -6 = -16 -16 + 2y + 3y = 8 + 7(y + -4) Combine like terms: 2y + 3y = 5y -16 + 5y = 8 + 7(y + -4) Reorder the terms: -16 + 5y = 8 + 7(-4 + y) -16 + 5y = 8 + (-4 * 7 + y * 7) -16 + 5y = 8 + (-28 + 7y) Combine like terms: 8 + -28 = -20 -16 + 5y = -20 + 7y Solving -16 + 5y = -20 + 7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7y' to each side of the equation. -16 + 5y + -7y = -20 + 7y + -7y Combine like terms: 5y + -7y = -2y -16 + -2y = -20 + 7y + -7y Combine like terms: 7y + -7y = 0 -16 + -2y = -20 + 0 -16 + -2y = -20 Add '16' to each side of the equation. -16 + 16 + -2y = -20 + 16 Combine like terms: -16 + 16 = 0 0 + -2y = -20 + 16 -2y = -20 + 16 Combine like terms: -20 + 16 = -4 -2y = -4 Divide each side by '-2'. y = 2 Simplifying y = 2
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