Question

5. Solve $2\left(\text{m}-5\right)-3\text{m}\left(2\text{m}-5\right)<5\text{m}+1$. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

Short answer

The solution set is$\left(\mathbf{0}.\mathbf{44},\infty \right)$.

The graph is:

Step-by-step solution

- State the definition of a variable.

A variable is a term that is used to represent an unknown value.

- Solve the inequality.

Here, the inequality is:

$2\left(m-5\right)-3\left(2m-5\right)<5m+1$

Simplify the inequality as shown below:

$\begin{array}{c}2\left(m-5\right)-3\left(2m-5\right)<5m+1\\ 2m-10-6m+15<5m+1\\ -4m+5<5m+1\\ -4m+5+4m<5m+1+4m\end{array}$

Now, subtract 1 from both sides,

$\begin{array}{c}-4m+5+4m<5m+1+4m\\ 5-1<9m+1-1\\ 4<9m\\ m>0.44\end{array}$

The solution set using interval notation is: $\left(0.44,\infty \right)$.

- Graph the solution set.

The solution set is: $\left(0.44,\infty \right)$.

Therefore, the graph of the solution set is: