Question

For what values of $x$ the given inequality $7x+5\le 5x+15$ is satisfied. When

Answer 1

Given: $7x+5\le 5x+15$
$\Rightarrow 7x+5-5x\le 5x+15-5x\left[\text{subtracting}5x\text{from both the sides of inequality}\right]$
$\Rightarrow 2x+5\le 15$
$\Rightarrow 2x+5-5\le 15-5\left[\text{subtracting}5\text{from both the sides of inequality}\right]$
$\Rightarrow 2x\le 10$
$\Rightarrow \frac{2x}{2}\le \frac{10}{2}\left[\text{divide both sides of inequality by}2\right]$
$\Rightarrow x\le 5$

Now we will check for every option
$\left(i\right)x\in N\text{set of natural numbers}$
$\therefore x\le 5$
$\Rightarrow x\in \{1,2,3,4,5\}$

$\left(ii\right)x\in W\text{set of whole numbers}$
$\therefore x\le 5$
$\Rightarrow x\in \{0,1,2,3,4,5\}$

$\left(iii\right)x\in Z\text{set of integers}$
$\therefore x\le 5$
$\Rightarrow x\in \{\cdots ,-3,-2,-1,0,1,2,3,4,5\}$

$\left(iv\right)x\in N\text{set of real numbers}$
$\therefore x\le 5$
$\Rightarrow x\in (-\infty ,5]$