 # Math

2021-09-28

Describe the error in solving the equation for x. • In the third step, the left side was not divided by −2−2 correctly.

• In the third step, the negative sign was not distributed to both terms in parentheses.

• The equation is not solved for xx because there is still a term with xx on both sides.

• The equation cannot be solved for xx because the terms with xx cancel out on each side.

### Question 2

Correct the error.

x=

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$$12−2x=−2(y−x)$$

Simplify $$−2(y−x)-2(y-x).$$

Rewrite.

$$12−2x=0+0−2(y−x)$$

$$12−2x=−2(y−x)$$

Apply the distributive property.

$$12−2x=−2y−2(−x)$$

Multiply $$−1$$ by $$−2$$.

$$12−2x=−2y+2x$$

Move all terms containing x to the left side of the equation.

Subtract $$2x$$ from both sides of the equation.

$$12−2x−2x=−2y$$

Subtract 2x from −2x.

$$12−4x=−2y$$

Subtract $$12$$ from both sides of the equation.

$$−4x=−2y−12$$

Divide each term in $$-4x=-2y-12$$ by $$-4$$ and simplify.

$$\frac{-4x}{4}=\frac{-2y}{-4}+\frac{-12}{-4}$$

Simplify the left side.

$$x=\frac{-2y}{-4}+\frac{-12}{-4}$$

Simplify the right side.

$$x=\frac{y}{2}+3$$