Question
Solve the following inequation and represent the solution set on the number line:
$
4 x-19<\frac{3 x}{5}-2 \leq-\frac{2}{5}+x, x \in R
$
$
4 x-19<\frac{3 x}{5}-2 \leq-\frac{2}{5}+x, x \in R
$
✓
Answer
$
4 x-19<\frac{3 x}{5}-2 \leq-\frac{2}{5}+x, x \in R
$
Hence, solution set is {x : -4 < x < 5, x ∈ R}
The solution set is represented on the number line as below.
$
\begin{aligned}
& \Rightarrow 4 x-19<\frac{3 x}{5}-2 \text { and } \frac{3 x}{5}-2 \leq \frac{-2}{5}+x, x \in R \\
& \Rightarrow 4 x-\frac{3 x}{5}<17 \text { and } 2+\frac{2}{5} \leq x-\frac{3 x}{5}, x \in R \\
& \Rightarrow \frac{17 x}{5}<17 \text { and } \frac{-8}{5}<\frac{2 x}{5}, x \in R \\
& \Rightarrow x <5 \text { and }-4 \leq x , x \in R \\
& \Rightarrow-4 \leq x <5, x \in R
\end{aligned}
$
Hence, solution set is $\{x:-4 \leq x<5, x \in R\}$
The solution set is represented on the number line as below.
4 x-19<\frac{3 x}{5}-2 \leq-\frac{2}{5}+x, x \in R
$
Hence, solution set is {x : -4 < x < 5, x ∈ R}
The solution set is represented on the number line as below.
$
\begin{aligned}
& \Rightarrow 4 x-19<\frac{3 x}{5}-2 \text { and } \frac{3 x}{5}-2 \leq \frac{-2}{5}+x, x \in R \\
& \Rightarrow 4 x-\frac{3 x}{5}<17 \text { and } 2+\frac{2}{5} \leq x-\frac{3 x}{5}, x \in R \\
& \Rightarrow \frac{17 x}{5}<17 \text { and } \frac{-8}{5}<\frac{2 x}{5}, x \in R \\
& \Rightarrow x <5 \text { and }-4 \leq x , x \in R \\
& \Rightarrow-4 \leq x <5, x \in R
\end{aligned}
$
Hence, solution set is $\{x:-4 \leq x<5, x \in R\}$
The solution set is represented on the number line as below.
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