Question

plz solve the following question​

Answer 1

Answer:

$\bold{ \large{x \: \in \: ( - 5,2 \: ]}}$

Step-by-step explanation:

$\frac{3}{5} x + 2 < x + 4 \leq \frac{x}{2} + 5$

Here we have 3 cases

$(1) \frac{3}{5} x + 2 < x + 4$

$= > \frac{2}{5} x > - 2$

$= > x > - 5$

$= > x \in \: ( - 5, \infty) \quad \{1 \}$

$(2) \frac{3}{5} x + 2 \leq \frac{x}{2} + 5$

$= > \frac{x}{10} \leq3$

$= > x \leq30$

$= > x \in \: ( - \infty,30] \quad \{2 \}$

$(3) x + 4 \leq \frac{x}{2} + 5$

$= > \frac{x}{2} \leq1$

$= > x \leq2$

$= > x \in \: ( - \infty,2] \quad \{3 \}$

$\text{combining \: \{1\} \: \{2\} \: and \: \{3\} \: we \: get}$

$\large{ \bold{= > x \in( - 5,2 \: ]}}$

Hope it helps