Solve the following linear inequations in R: Solve: 4x - 2 < 8, w… - Vidyadip

Question

Solve the following linear inequations in $R:$
Solve: $4x - 2 < 8,$ when

$\text{x}\in\text{R}$
$\text{x}\in\text{N}$
$\text{x}\in\text{N}$

✓

Answer

Now,
$4x - 2 < 8$
$\Rightarrow 4x < 8 + 2$
$\Rightarrow 4x < 10$
$\Rightarrow\text{x}<\frac{10}{4}=\frac{5}{4}$

If $\text{x}\in\text{R},$ then $\text{x}<\frac{5}{2}\Rightarrow\text{x}\in\Big(-\infty,\frac{5}{2}\Big)$
If $\text{x}\in\text{Z},$ then $\text{x}<\frac{5}{2}\Rightarrow\text{x}\in\{...,-2,-1,0,1,2\}$
If $\text{x}\in\text{N},$ then $\text{x}<\frac{5}{2}\Rightarrow\text{x}\in\{1,2\}$

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