40r-22=63r-91 can you help me find r and show me how to do it please?

Question

I need help with the answer please

 

Answer 1

Hi Kasey, here is the solution

40 r - 22 = 63 r - 91

40 r - 63 r =22 - 91    by isolating terms containing r on one side and the constants on the other side

-23 r = -69  by combining like terms

r = -69/-23   by dividing both sides by -23

r = 3   the answer

Answer 2

Hi Kasey!  Just think something like, "I need to collect all the terms that look similar all together."  In this case, 40r and 63r both look similar, because they both have the letter r, and the other terms don't.  And since the other two terms, -22 and -91 (don't forget the +/- signs!) also look similar (have no letter with them), they can go together.  The other thing to ALWAYS remember in algebra or any equation:  it must stay balanced - that means whatever you do to one side you also have to do to the other.

 

40r - 22 = 63r - 91

Let's subtract 40r from both sides (to keep that balance):  40r-40r - 22 = 63r-40r - 91

Why did we do this?  To get all the r's together.   Now we have  -22 = 23r -91

Now let's get the non-r's together, and get the r's to be alone by adding 91 to both sides:  

-22 + 91 = 23r -91 +91,   +69 = 23r

Now we only need to get r by itself.  So we can divide both sides by 23:  69/23 = 23r/23

3 = r, or r=3, our answer!

Now prove it's correct:  40(3) - 22 = 63(3) - 91;  120 - 22 = 189 - 91;   98 = 98  (Hooray - we're right!)

 

Answer 3

The key these Algebra questions is to get all of the "r" terms on one side and the number terms on the other side of the equations here's how we do it:

40r-22 = 63r-91

I like to put the letters on the left hand side so lets subtract 63r from both sides

40r-22-63r = 63r-91-63r

this gives us

-23r-22 = -91

now isolate the "r" term by adding 22 to both sides

-23r-22+22=-91+22

this gives us 

-23r = -69

divide both sides by -23 and you will have the solution

r = 3

Answer 4

40r - 22 = 63r - 91                     Given

40r - 22 + 22 = 63r - 91 + 22      Addition 22 to each side

40r + 0 = 63r - 91 + 22               Inverse property of addition

40r = 63r - 91 + 22                     Identity property of addition

40r = 63r - 69                             Simplify (-91 + 22 = 69)

40r - 63r = 63r - 69 - 63r             Subtract 63r from each side

40r - 63r = 0 - 69                        Inverse property of addition

40r - 63r = -69                            Identity property of addition

-23r = -69                                   Simplify (40r - 63r = -23r)

-23r/(-23) = -69/(-23)                  Divide each side by -23

r = -69/(-23)                                Inverse property of multiplication

r = 3                                            Simplify (-69/-23 = 3)