Question

6-9/7x>8

Answer 1

\(6-\dfrac{9}{7}x>8\)
If this were an equation instead of an inequality, would you know how to solve it?

Answer 2

no bc im not good with fractions but this is what i got x<1 1/5

Answer 3

Ok, I can help you. Give me a minute to solve it.

Answer 4

The first step will be to move the constant term (6) to the right by using inverse operations - because it is positive, you will subtract 6 from both sides.

Answer 5

What did you get from that step?

Answer 6

-9/7x>2

Answer 7

Great! Now you want to separate the fraction from the x term. You will do that by dividing both sides by -9/7.
Two things to remember:
1. When you divide an inequality by a negative - the inequality reverses. (I think you already knew that)
2. When you divide by a fraction, you actually multiply by its inverse.

Answer 8

FYI:

\(8\div 2 = 8 \times \dfrac{1}{2}\)
\(\dfrac{1}{2}\) is the inverse of 2

Answer 9

Your next step in this inequality will look like this:
\(-\dfrac{9}{7}\div-\dfrac{9}{7}x >2 \div -\dfrac{9}{7}\)

Answer 10

Same \(\implies\) Change \(\implies\) Flip
Keep the first fraction the same, change the division to multiplication, flip the second fraction.
Give that a try and let me know what you get.

Answer 11

x<1 1/5

Answer 12

Not quite.

Answer 13

On the left side, the fractions will cancel out - on the right side, you multiply straight across:
\(-\dfrac{9}{7}\times-\dfrac{7}{9}x < 2 \times -\dfrac{7}{9}\)

Answer 14

-14/9

Answer 15

Yes. You probably need to answer in simplest terms, so that would mean to change the improper fraction to a mixed number.

Answer 16

1 1/9 would be the answer

Answer 17

Yes, that is the answer I got.
Except that it is still negative. Got to watch out for those pesky negatives, they are slippery and tend to fall on the floor. :-)

Answer 18

Do you understand the answer? Would you like more help with fractions?

Answer 19

thank you so much!

Answer 20

You're welcome.

Answer 21

if this was an inequality would i flip the sign