How do you solve and write the following in interval notation: # | 5x + 3 | 18#?

Question

How do you solve and write the following in interval notation:  # | 5x + 3  | >18#?

Eva Adamson · Accepted Answer

When you have the absolute value, you can remove it considering the two sign #\pm#. You have to be careful with the inequality because the #+# keep the direction of the inequality while the #-# inverte it. In your case you have #|5x+3|>18# #5x+3>18# and #5x+3<-18# #5x>15# and #5x<-21# #x>3# and #x<-21/5#. As interval you can say that #x in (-oo, -21/5) and (3, +oo)#.

Jace Anderson · Answer

undefined To solve the inequality $ |5x + 3| > 18 $, you can follow these steps: 1. Split the absolute value inequality into two separate inequalities: $ 5x + 3 > 18 $ and $ 5x + 3 < -18 $ 2. Solve each inequality individually: $ 5x + 3 > 18 $ Subtract 3 from both sides: $ 5x > 15 $ Divide by 5: $ x > 3 $ $ 5x + 3 < -18 $ Subtract 3 from both sides: $ 5x < -21 $ Divide by 5: $ x < -\frac{21}{5} $ 3. Write the solutions in interval notation: For $ x > 3 $, the interval notation is $ (3, \infty) $ For $ x < -\frac{21}{5} $, the interval notation is $ (-\infty, -\frac{21}{5}) $ So, the solution to $ |5x + 3| > 18 $ in interval notation is $ (-\infty, -\frac{21}{5}) \cup (3, \infty) $.

How do you solve and write the following in interval notation: # | 5x + 3 | &gt;18#?

How do you solve and write the following in interval notation: # | 5x + 3 | >18#?