Question

Solve the inequality. Graph and check your solution.

$\mathbf{4}\mathbf{x}\mathbf{+}\mathbf{1}\mathbf{>}\mathbf{1}$

Short answer

Solution of the inequality is $x>0$.

Step-by-step solution

Step-1- Solve the inequality

$\begin{array}{c}4x+1>1\\ 4x+1-1>1-1\left(\text{Subtract1frombothsides}\right)\\ 4x>0\\ x>0\left(\text{Dividebothsidesby4}\right)\end{array}$

Step-2- Graph the inequality

The solution of the inequality is$x>0$.

That means, all values$x>0$ satisfy the inequality. So, the graph can be given as shown below.

Step-3- Check the solution

To check the solution, take any random number,$x>0$ and substitute in the original inequality and observe the result.

Take$x=2$.

Then,

$\begin{array}{c}4\times 2+1>1\\ 8+1>1\\ 9>1\end{array}$

Observe that 9 is greater than 1. So, the result is true and hence the solution is correct.