How do you solve #|12- 5x |

Question

How do you solve #|12- 5x | < 22#?

Savannah Anderson · Accepted Answer

#-2 < x< 34/5# #|12-5x|<22# means either #12-5x<22# i.e. #12-22<5x# i.e. #5x> -10# i.e. #x> -2# or #-(12-5x)<22# i.e. #-12+5x<22# i.e. #5x< 22+12# i.e. #5x<34# i.e. #x<34/5# Hence either #x> -2# or #x< 34/5#, which can be combined as #-2 < x< 34/5#

Eva Abramson · Answer

#-2 < x< 34/5#

This can be interpreted as

#-5x+12<22# and #-5x+12> -22#

We can subtract #12# from both sides in both inequalities to get

#-5x<10# and #-5x> -34#

Next, we can divide both sides by #-5#. Recall the direction of the inequality will flip. We get

#x> -2# and #x< 34/5#

We can combine these to get

#-2 < x < 34/5#

Hope this helps!

Abigail Allen · Answer

undefined To solve the inequality $|12 - 5x| < 22$: 1. Split the inequality into two cases: a. $12 - 5x < 22$ b. $-(12 - 5x) < 22$ 2. Solve each case separately: a. For $12 - 5x < 22$: $12 - 5x < 22$ $-5x < 22 - 12$ $-5x < 10$ $x > -2$ b. For $-(12 - 5x) < 22$: $-(12 - 5x) < 22$ $12 - 5x > -22$ $-5x > -22 - 12$ $-5x > -34$ $x < 6.8$ 3. Combine the solutions from both cases: $x > -2$ and $x < 6.8$ So, the solution to the inequality $|12 - 5x| < 22$ is $-2 < x < 6.8$.

How do you solve #|12- 5x | &lt; 22#?

How do you solve #|12- 5x | < 22#?