| -x + 3 | ≥ 7

2 Answers

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should remember that the algorithm you need to follow when you solve the absolute value equation is similar to the algorithm used when solving an absolute value inequality.

You need to set up to cases such that:

`-x +3 gt= 7 or -x + 3lt= -7`

`` Solving the right inequality yields:

`-x + 3 gt= 7 =gt -x gt=-3 + 7 =gt -x gt= 4 =gt xlt= -4`

Solving the left inequality yields:

`-x + 3<= -7 =gt -x<= -3 - 7 =gt -x<= -10 =gt x gt= 10` 

Hence, the solution to the absoute value inequality is: `(-oo, -4]U[10, +oo).`

beckden's profile pic

beckden | High School Teacher | (Level 1) Educator

Posted on

We split the absolute value into two

`-x+3gt=7` or `-x+3lt=-7`

Adding -3 to both sides of both equations

`-xgt=4` or `-xlt=-10`

Multiply both sides by -1 (and reverse the direction of the inequalities) we get

`xlt=-4` or `xgt=10`