# How do you solve " difference of 5 times a number and 6 is greater than the number." and graph the solution on a number line?

Jun 14, 2018

$x > \frac{3}{2}$

#### Explanation:

I'll try to split the text chunk by chunk, and translate it into formula:

"Difference of..." $\setminus \to$ I have to subtract the next two things

"$5$ times a number" $\setminus \to 5 x$

"$6$" $\setminus \to 6$ (well that was obvious)

"is greater than..." $\setminus \to >$

"the number" $\setminus \to x$

So, the inequality is

$5 x - 6 > x$

We can subtract $x$ from both sides..

$4 x - 6 > 0$

Add $6$ to both sides..

$4 x > 6$

And divide both sides by $4$ to get

$x > \frac{6}{4} = \frac{3}{2}$

This means that we accept all the numbers which are greater than $\frac{3}{2}$

On a number line, you only need to find $\frac{3}{2}$ and accept all the numbers from there on.