How do I solve this problem?       `-2/3x=5`

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txmedteach's profile pic

txmedteach | High School Teacher | (Level 3) Associate Educator

Posted on

So here, we need to figure out what value for `x` will allow the following equation to be true:

`-2/3x = 5`

We need to answer the question "Negative two-thirds of what number is 5?"

Well, we can manipulate this a number of ways. We can start by multiplying both sides by 3 to get rid of the fraction. Remember, if you have a fraction with the same factor in the numerator and denominator, you can cancel them out!

`-(3*2)/3 x= 3*5`

`-2 x=15`

Now, we're going to do the same thing, but with division. We're going to divide both sides by -2 so we can cancel out the -2 with x:

`-2/-2x = 15/-2`

`x = -15/2`

We can't simplify the fraction much further. We can get a decimal though!

`x = -7.5`

So, there's our answer. A quicker option, if you understand what we just did, is to multiply by the multiplicative inverse of the fraction. In our case, that would mean multiplying by `-3/2`:

`-3/2*-2/3 x = -3/2*5`

This pretty much combines the two steps we took into one step. We get the same answer, but it's just quicker if you undestand how it works!

I hope that helps!


zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on


Since you are trying to isolate x do the inverse 




jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

-2/3x = 5

To get " x " alone I will have to divide -2/3 on both sides

5 X -3/2 = -15/2

By dividing on both sides , your equation should look like :

x = -15/2 which is your answer ; you can also change it into a mixed number which is -7 1/2

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nisarg | Student, Grade 11 | (Level 1) Valedictorian

Posted on




``multiply both sides by 3 then divide by -2

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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We need to isolate x. To do this, we have to undo whatever is being done to x. Right now, x is being multiplied by -2/3 . To undo this, we have to divide by -2/3. Which is the same as multiplying by the reciprocal -3/2. 

x = 5(-3/2)

x = -15/2

zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`-2/3x` = 5

Solve for the variable

do the inverse fraction

`(3/2)` (-`2/3x)` = 5 `(3/2)`


atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

fist you multiply the 2 sides by the denominator to get rid of the fraction

`3xx -2/3 x = 5xx3 `

this will cancel the 3


now divide by -2 to get x by itself


x= -7.5

or -7 1/2

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