Question

Solve each inequality. Check your solution.

$4<\frac{c}{5}$

Short answer

The required value of c is $\left(20,\infty \right)$.

Step-by-step solution

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{or}\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$$\begin{gathered} 1.b\le c\Rightarrow b\pm a\le c\pm a \\ 2.b\le c\Rightarrow ab\le ac,\text{if}a>0 \\ 3.b\le c\Rightarrow ab\ge ac,\text{if}a<0 \end{gathered}$$

Step 2. Solve the inequality for x.

In order to solve the inequality:

$\frac{1}{3}y\le 5$

Multiply both sides by 5, as

$$\begin{gathered} 4<\frac{c}{5} \\ 4\times 5<\frac{c}{5}\times 5 \\ 20<c \\ c>20 \end{gathered}$$

Thus, the inequality is true for c greater than 20, thus the solution of given inequality in interval form is, as $\left(20,\infty \right)$.

Step 3. Check the solution.

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting c equals to 20 in right hand side

$$\begin{gathered} \frac{20}{5}=4 \\ =\text{LeftHandside} \end{gathered}$$

Now put any value any value of c greater than 20, say 30 and check whether it satisfies the inequality, as

$$\begin{gathered} 4<\frac{c}{5} \\ 4<\frac{30}{5} \\ 4<6\left[\text{True}\right] \end{gathered}$$

Since, both conditions are satisfied thus solution of inequality is correct.