How do you solve and write the following in interval notation: #|-4x| + |-5| <=9#?

1 Answer
May 9, 2017

Answer:

Solve for #|x|# and find the bounds for which #x# must lie in.

Explanation:

Since constants can be taken out of absolute values are their positive values when alone or when multiplied with a variable (but not when adding/subtracting), we can rewrite the inequality as:
#4|x|+5<=9#

Now we solve for #|x|#:
#|x|<=1#

We can remove the absolute value by recognizing that #x# must be equal to or between #-1# and #1#:
#-1<=x<=1#

In interval notation, parentheses are used for greater than (>), less than (<), and infinity (both #-oo# and #oo#). Brackets are used for greater than or equal to (#>=#) and less than or equal to (#<=#).
Therefore, #-1<=x<=1# can be written as #[-1,1]# in interval notation.