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?

Question

Abigail Allen · Accepted Answer

#x>3/2#

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.

Eva Abramson · Answer

undefined To solve the inequality "difference of 5 times a number and 6 is greater than the number," we first express it as an inequality:

5x - 6 > x

Then, we solve for x:

5x - x > 6
4x > 6
x > 6/4
x > 3/2

So, the solution to the inequality is x > 3/2. To graph this solution on a number line, we mark an open circle at 3/2 and shade to the right to indicate all numbers greater than 3/2.