Question

solve the following inequality for x and illustrate the solution with diagram.
1) 2x+1<5
b) 5x-3<_11​

Answer 1

$\huge{ \blue{ \boxed{\green{\mathbb{SOLUTION}}}}}$

$\huge{ \blue{ \boxed{\green{\mathbb{1.}}}}}$

$\blue{ \sf \: 2x + 1 < 5}$

$\pink{ \mathcal{ \: Substract \: \: 1 \: \: to \: \: both \: \: sides}}$

$\blue{ \rightarrow\sf \: 2x + 1 - 1 < 5 - 1}$

$\blue{ \rightarrow\sf \: 2x < 4}$

$\pink{ \mathcal{ \: Divide \: \: both \: \: sides \: \: by \: \: 2}}$

$\blue{ \rightarrow\sf \: \frac{2x}{2} < \frac{4}{2} }$

$\blue{ \rightarrow \boxed{\sf \: x < 2}}$

$\green{ \rightarrow \boxed{\sf \: x \in ( - \infty \: 2)}}$

$\huge{ \blue{ \boxed{\green{\mathbb{2.}}}}}$

$\blue{ \sf \: 5x - 3\leqslant 11}$

$\pink{ \mathcal{ \: Add \: \: both \: \: side \: \: by \: \: 3}}$

$\blue{ \rightarrow \sf \: 5x - 3 + 3\leqslant 11 + 3}$

$\blue{ \rightarrow \sf \: 5x \leqslant 14}$

$\pink{ \mathcal{ \: Divide \: \: both \: \: sides \: \: by \: \: 5}}$

$\blue{ \rightarrow \sf \: \frac{5x}{5} \leqslant \frac{14}{5} }$

$\blue{ \rightarrow \sf \: x \leqslant \frac{14}{5} }$

$\green{ \rightarrow \boxed{\sf \: x \in ( - \infty \: \frac{14}{5} )}}$

${ \blue{ \boxed{\green{\mathbb{Varified \: \: Answer }}}}}$