Question

Describe and correct the errors in solving the absolute value inequality

х

5x + 4/> 13

x+4 -13 and x + 4 <13

x>-17 and

X<9

-17
22

There is an arithmetic error in both rewritten inequalities. The correct solution is -9<< < 17

The inequality symbols should be reversed. The correct solution is 9 > I > -17

The two inequalities should be written as one inequality -13 < 3+4 < 13. The correct solution is -17 <3 <9.

The compound inequalities should be joined by "or;" and both inequality symbols should be reversed. The correct solution is

< 17 ore 9.

Answer 1

Explanation:

Given the inequality
`|x+4|>13`, to solve, we will solve the negative and positive value of the modulus for x as shown:

If the modulus is positive:

`x+4>13\\`

subtract 4 from both sides

`x+4-4>13-4\\x>9`

If the modulus is negative

`-(x+4)>13\\-x-4>13\\`

Add 4 to both sides

`-x-4+4>13+4\\-x>17`

Multiply both sides by -1

`-(-x)<-17\\x<-17\\-17>x`

Combine both inequalities. If:

`x>9\\`

Combining with
`-17>x` will give:

`-17>x>9`