Question

Solve the equations and graph the solution

Answer 1

Given:

The inequalities are:

$-5x$ or $2x$

To find:

The solution for the given inequalities and graph the solution.

Solution:

We have,

$-5x$ or $2x$

Solve the above inequalities separately.

$-5x$

Divide both sides by -5.

$x>\dfrac{-3}{-5}$

$x>\dfrac{3}{5}$             ...(i)

And,

$2x$

Divide both sides by 2.

$x$

$x$                       ...(ii)

From (i) and (ii). we get

$x$ or $x>\dfrac{3}{5}$

The interval notation of the solution is $(-\infty,-4)\cup \left(\dfrac{3}{5},\infty\right)$.

The graph of the solution is shown below.