Answer:
[tex]x>\frac{83}{15}[/tex]
Step-by-step explanation:
STEP 1: Simplify [tex]\frac{x-5}{2} +\frac{2}{5}>\frac{2}{3}[/tex]
[tex]\frac{5x-21}{10}>\frac{2}{3}[/tex]
STEP 2: Multiply both sides of the equation by [tex]10[/tex].
[tex]\frac{5x-21}{10}>\frac{2}{3}*(10)[/tex]
STEP 3: Remove parentheses.
[tex]\frac{5x-21}{10}>\frac{2}{3}*(10)[/tex]
STEP 4: Multiply [tex]\frac{2}{3}*(10)[/tex]
[tex]\frac{5x-21}{10}>\frac{20}{3}[/tex]
STEP 5: Move all terms not containing [tex]x[/tex] to the right side of the inequality.
[tex]5x>\frac{83}{3}[/tex]
STEP 6: Divide each term by [tex]5[/tex] and simplify.
[tex]x>\frac{83}{15}[/tex]
STEP 7: The result can be shown in multiple forms.
Inequality Form:
[tex]x>\frac{83}{15}[/tex]
Interval Notation:
[tex](\frac{83}{15}[/tex],∞[tex])[/tex]
