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Simplifying 7(y + 2) + -6(x + -5) = 5(y + 5) + 3(y + -2) Reorder the terms: 7(2 + y) + -6(x + -5) = 5(y + 5) + 3(y + -2) (2 * 7 + y * 7) + -6(x + -5) = 5(y + 5) + 3(y + -2) (14 + 7y) + -6(x + -5) = 5(y + 5) + 3(y + -2) Reorder the terms: 14 + 7y + -6(-5 + x) = 5(y + 5) + 3(y + -2) 14 + 7y + (-5 * -6 + x * -6) = 5(y + 5) + 3(y + -2) 14 + 7y + (30 + -6x) = 5(y + 5) + 3(y + -2) Reorder the terms: 14 + 30 + -6x + 7y = 5(y + 5) + 3(y + -2) Combine like terms: 14 + 30 = 44 44 + -6x + 7y = 5(y + 5) + 3(y + -2) Reorder the terms: 44 + -6x + 7y = 5(5 + y) + 3(y + -2) 44 + -6x + 7y = (5 * 5 + y * 5) + 3(y + -2) 44 + -6x + 7y = (25 + 5y) + 3(y + -2) Reorder the terms: 44 + -6x + 7y = 25 + 5y + 3(-2 + y) 44 + -6x + 7y = 25 + 5y + (-2 * 3 + y * 3) 44 + -6x + 7y = 25 + 5y + (-6 + 3y) Reorder the terms: 44 + -6x + 7y = 25 + -6 + 5y + 3y Combine like terms: 25 + -6 = 19 44 + -6x + 7y = 19 + 5y + 3y Combine like terms: 5y + 3y = 8y 44 + -6x + 7y = 19 + 8y Solving 44 + -6x + 7y = 19 + 8y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-44' to each side of the equation. 44 + -6x + -44 + 7y = 19 + -44 + 8y Reorder the terms: 44 + -44 + -6x + 7y = 19 + -44 + 8y Combine like terms: 44 + -44 = 0 0 + -6x + 7y = 19 + -44 + 8y -6x + 7y = 19 + -44 + 8y Combine like terms: 19 + -44 = -25 -6x + 7y = -25 + 8y Add '-7y' to each side of the equation. -6x + 7y + -7y = -25 + 8y + -7y Combine like terms: 7y + -7y = 0 -6x + 0 = -25 + 8y + -7y -6x = -25 + 8y + -7y Combine like terms: 8y + -7y = 1y -6x = -25 + 1y Divide each side by '-6'. x = 4.166666667 + -0.1666666667y Simplifying x = 4.166666667 + -0.1666666667y
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