Answer:
[tex]\left[ \dfrac{4}{3},4 \right][/tex]
Step-by-step explanation:
Inequality 1
[tex]3y-13\geq -9[/tex]
Add 13 to both sides:
[tex]\implies 3y-13+13\geq -9+13[/tex]
[tex]\implies 3y\geq 4[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}\geq \dfrac{4}{3}[/tex]
[tex]\implies y \geq \dfrac{4}{3}[/tex]
Therefore, y is equal to or bigger than 4/3.
Inequality 2
[tex]3y-13\leq -1[/tex]
Add 13 to both sides:
[tex]\implies 3y-13+13\leq -1+13[/tex]
[tex]\implies 3y\leq 12[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}\leq \dfrac{12}{3}[/tex]
[tex]\implies y\leq 4[/tex]
Therefore, y is equal to or smaller than 4.
Therefore, the solution to the inequalities in interval notation is:
[tex]\left[ \dfrac{4}{3},4 \right][/tex]
