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what is the answer for this inequalities 4r-9>7

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1 Answer

Eugena,

When you are working with an equation involving inequalities (<,>) you can treat it just like an equation with an = sign.  So we can use the same rules, and we will be trying to get the r "by itself".  In order to do this we have to do the opposite of whatever is happening to r to both sides of our equation.  

Currently we are subtracting 9 from the r side of the equation, so we will add 9 to each side giving us,

4r-9+9>7+9

4r>16.

Now we are multiplying r by 4, so we will divide both sides by 4.  This gives us,

(4r)/4>16/4

r>4.

I hope this helps!

Comments

While this is a correct answer for solving this particular problem, be very careful with this. I agree that it is helpful to think of inequalities as being like equations. But they are actually two distinct things, and you want to get your terminology correct.

Next while it is true that you can solve this inequality by treating it just like an equation, that is not true for all inequalities. If you have to multiply or divide by a negative number, then you have to change the direction of the inequality. For example, if this were -4r - 9 > 7 instead, we would solve it slighting differently:

-4r - 9 + 9 > 7 + 9
-4r > 16
(-4r)/-4 < 16/-4 (notice we changed from > to < on this step!)
r < -4

So while this solution works, you can't just say that inequalities can always be treated just like equations.

Thank you for your comment Brian.  I was simply explaining how to work through this problem, but it is good to point out that in solving different problems a different method is needed.  

Eugena, I hope our tag-teamed response helps!

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