Question

Analyze the solution shown.1. –|–x| = 7: given

2. |–x| = –7: multiplication property of equality

3. –x = 7 or –x = –7: definition of absolute value

4. x = –7 or x = 7: multiplication property of equality

5. Check: –|–(–7)| = 7, –7 ≠ 7

–|–7| = 7, 7 = 7

Negative times negative is positive.

Answer 1

They are all correct steps

Answer 2

Answer with explanation:

The given expression is:

- | -x|=7

Multiplying both sides by , -1

2. | -x|= -7 →Multiplication property of equality

3. –x = 7 or –x = –7:⇒ definition of absolute value

Because , |x|=x, if , x>0

and, -x, if x<0.

Multiplying by, -1 on both sides of equation 1, and Dividing by , -1 on both sides

4. → x= -7, or, →x=7

⇒To Check:

L HS for, x = -7

= - | -(-7)|

= - | 7|

= -7 ≠ R HS

So, x= -7, is not the solution of the system of equation.

⇒L HS , for x=7

= - | (-7)|

= - 7 ≠ R HS

There is no such , x for which, –|–x| = 7.Because Modulus is always a positive Quantity. Negative sign before any Positive number can't give positive number.