The inequality given is
[tex]4x+3<-\frac{5x}{4}+5[/tex]
We take all the variables to one side and numbers to another. Then we solve it. The steps are shown below:
[tex]\begin{gathered} 4x+3<-\frac{5x}{4}+5 \\ 4x+\frac{5x}{4}<5-3 \\ \frac{21}{4}x<2 \\ x<\frac{2}{\frac{21}{4}} \\ x<2\times\frac{4}{21} \\ x<\frac{8}{21} \end{gathered}[/tex]
Solution
[tex]x<\frac{8}{21}[/tex]
Now, in interval notation, we can write,
[tex](-\infty,\frac{8}{21})[/tex]
The graph of the solution in a number line would be all numbers LESS THAN 8/21.
Choice E shows this correctly.
Remember, in graph, "(" or ")" shows a number that isn't included.
"[" or "]" shows a number that is included.
Answer------>>> Solution
[tex]x<\frac{8}{21}[/tex]
------>>> Solution (in interval notation)
[tex](-\infty,\frac{8}{21})[/tex]
------>>> Solution (Graph)
E
