Question

Solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) - 3y + 3]

Accepted Answer

Start by expanding the expressions inside the brackets on both sides of the equation. For the left side, distribute the -3 across the terms inside the parentheses: $$-3(y + 2)$$ becomes $$-3y - 6. $$For the right side, distribute the -3 across $$2y - 5$$ and also expand the terms inside the brackets: $$5(y - 1)$$ becomes $$5y - 5. $$Rewrite the equation after expansion: $$25 - [2 + 5y - 3y - 6] = -3(2y - 5) - [5y - 5 - 3y + 3]. $$Then simplify inside the brackets by combining like terms: on the left, combine $$5y - 3y$$ and constants; on the right, combine $$5y - 3y$$ and constants inside the brackets. Remove the brackets by applying the subtraction sign outside the brackets on the left side and the negative sign on the right side. This means changing the signs of the terms inside the brackets accordingly. Combine like terms on both sides of the equation to simplify it into the form $$ay + b = cy + d$$, where $$a$$, $$b$$, $$c$$, and $$d$$ are constants. Isolate the variable $$y by $$moving all terms containing $$y to $$one side and constants to the other side. Then solve for $$y by $$dividing both sides by the coefficient of $$y.$$

Solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) - 3y + 3]

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Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations