Answer :
We have the function:
[tex]f(x)=5+|2x-5|\text{.}[/tex]We must find all the x for which we have:
[tex]f(x)<26.[/tex]1) Replacing the definition of f(x) in the inequality, we have:
[tex]5+|2x-5|<26.[/tex]2) Solving for x, we get:
[tex]\begin{gathered} |2x-5|<26-5, \\ |2x-5|<21, \\ -21<2x-5<21, \\ -21+5<2x<21+5, \\ -16<2x<26, \\ -\frac{16}{2}The solution is the set of values of x that are greater than -8 and smaller than 13. In interval notation: (-8, 13).Plotting the points, we get the following graph:
Answer
• The solution are the values of x such that: ,-8 < x < 13,.
,• Or the points in the interval ,(-8, 13),.
,• Graph
