Question
Solve the following inequation and graph the solution set,
2x - 5 ≤ 5x + 4 < 11n ∈ R.
2x - 5 ≤ 5x + 4 < 11n ∈ R.
✓
Answer
Here, 2x - 5 ≤ 5x + 4 < 11
⇒ 2x - 5 ≤ 5x + 4 and 5x + 4 < 11
⇒ -3x < 9 and 5x < 7
⇒ x ≥ - 3 and x < $\frac{7}{5}$
$\therefore$ Solution set $=\left\{x:-3 \leq x \leq \frac{7}{5}\right.$ and $\left.x \in R \right\}$.
⇒ 2x - 5 ≤ 5x + 4 and 5x + 4 < 11
⇒ -3x < 9 and 5x < 7
⇒ x ≥ - 3 and x < $\frac{7}{5}$
$\therefore$ Solution set $=\left\{x:-3 \leq x \leq \frac{7}{5}\right.$ and $\left.x \in R \right\}$.
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