Question
Solve and graph the solution set on a number line : $\frac{2}{3} \mathrm{x}+5 \leq \frac{1}{2} \mathrm{x}+6 ; \mathrm{x} \in \mathrm{W}$
✓
Answer
$\frac{2}{3} x+5 \leq \frac{1}{2} x+6$
$\Rightarrow \frac{2}{3} \mathrm{x} \times 6+5 \times 6 \leq \frac{1}{2} \mathrm{x} \times 6+6 \times 6 \ldots ($Multiplying both sides by $6 )$
$\Rightarrow 4 x+30 \leq 3 x+36$
$\Rightarrow 4 x-3 x+30 \leq 3 x-3 x+36 \ldots($ Substracting $3 x$ from both sides$)$
$\Rightarrow x+30 \leq 36$
$\Rightarrow x+30-30 \leq 36-30 \ldots ($Substracting $30$ from both sides$)$
$x \leq 6$
$\therefore$ The required graph is:
$\Rightarrow \frac{2}{3} \mathrm{x} \times 6+5 \times 6 \leq \frac{1}{2} \mathrm{x} \times 6+6 \times 6 \ldots ($Multiplying both sides by $6 )$
$\Rightarrow 4 x+30 \leq 3 x+36$
$\Rightarrow 4 x-3 x+30 \leq 3 x-3 x+36 \ldots($ Substracting $3 x$ from both sides$)$
$\Rightarrow x+30 \leq 36$
$\Rightarrow x+30-30 \leq 36-30 \ldots ($Substracting $30$ from both sides$)$
$x \leq 6$
$\therefore$ The required graph is:
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