Evaluate: (4)/(3) \times (f-(2)/(3)) <= (8)/(3)f+(4)/(9)

Expression: $\frac{ 4 }{ 3 } \times \left( f-\frac{ 2 }{ 3 } \right) \leq \frac{ 8 }{ 3 }f+\frac{ 4 }{ 9 }$

Distribute $\frac{ 4 }{ 3 }$ through the parentheses

$\frac{ 4 }{ 3 }f-\frac{ 8 }{ 9 } \leq \frac{ 8 }{ 3 }f+\frac{ 4 }{ 9 }$

Multiply both sides of the inequality by $9$

$12f-8 \leq 24f+4$

Move the variable to the left-hand side and change its sign

$12f-8-24f \leq 4$

Move the constant to the right-hand side and change its sign

$12f-24f \leq 4+8$

Collect like terms

$-12f \leq 4+8$

Add the numbers

$-12f \leq 12$

Divide both sides of the inequality by $-12$ and flip the inequality sign

$\begin{align*}&f \geq -1 \\&\begin{array} { l }f \in \left[ -1, +\infty\right\rangle\end{array}\end{align*}$