Question

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?

Answer 1

`x>3/2`

Explanation:

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

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

"`5` times a number" `\to 5x`

"`6`" `\to 6` (well that was obvious)

"is greater than..." `\to >`

"the number" `\to x`

So, the inequality is

`5x-6>x`

We can subtract `x` from both sides..

`4x-6>0`

Add `6` to both sides..

`4x>6`

And divide both sides by `4` to get

`x>6/4=3/2`

This means that we accept all the numbers which are greater than `3/2`

On a number line, you only need to find `3/2` and accept all the numbers from there on.