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2/3(4x-1)=-22

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3 Answers

2/3(4x-1)=-22  

The first thing you want to do to tackle this problem is to get rid of that fraction!  When solving equations, we can multiply the equation through by the least common denominator to eliminate fractions.  There's only one fraction here, so our LCD is 3:

3 * (2/3)(4x-1) = 3*-22

When I multiply 3 * (2/3) I'm left with the 2 from the top of the fraction.  Since (4x+1) is being multiplied in the original equation by (2/3), I don't have to multiply those terms by 3.  Now I have

2(4x-1) = -66

Now this looks easier to tackle, doesn't it?  I need to use the distributive property:

2(4x) - 2(1) = -66

8x - 2 = -66

And now we're into an easier equation to solve.  I bet you know how to finish from here!  Here is my work to finish:

8x - 2 + 2 = -66 + 2  (be careful with the negative!)

8x = -64

Divide both sides by 8 and get

x = -8

 

Do you know how to check your answer?  You can substitute the solution value back into the original equation and see if it 'works':

2/3(4(-8)  -1)=-22

Order of operations from here!

2/3 (-32 - 1) = -22

2/3 (-33) = -22

-22 = -22

Both sides came out the same, so I know my solution was correct.

 

Hope this helps!

Alright your first step is to carry 2/3 to the other side by muliplying both sides by 3/2.

Then you have:

(3/2)(2/3)(4x-1)=-22(3/2)

On the left side, (3/2)(2/3) gets cancelled out, so you have:

4x-1 = -22(3/2)

4x-1 = -66/2

4x-1 = -33

Then, you add 1 to both sides in order to bring the 1 over to the other side.

4x-1+1 = -33 +1

4x = -32

Now divide both sides by 4.

x = -32/4

x = -8


Hope this helps :)

 

Both answers above are great.

It just depends upon how your teacher wants you to solve the problem.

Here is one more way:

2/3 * (4x - 1) = -22

multiply the left side out

(2/3 * 4x) + (2/3 * -1) = -22

8x/3 - 2/3 = -22

Now you can do one of two things:

1. Find a common denominator for the entire problem, which luckily is 3,

and therefore, -22 can become -66/3 and the problem reads:

8x/3 - 2/3 = -66/3

then go to step 2.

OR

2. Multiply all by 3 to eliminate the fraction and the problem reads:

(3 * 8x/3) + (3 * -2/3) = -22 * 3

Either way, you get 8x - 2 = -66

Add 2 to both sides:  8x -2 +2 = -66 +2

8x = -64

Solve for x.

Divide both sides by 8

8x/8 = -64/8

x = -8

ALWAYS check your answer.  Plug in -8 for x.

2/3 * ( 4(-8) -1) = -22