`(3/2)x - -4 = 13` Solve the equation for x.

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txmedteach's profile pic

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

Posted on

To start this question, let's just rewrite it here quickly:

`3/2x - (-4) = 13`

Let's just simplify that minus negative 4 (remember, -- = +):

`3/2x+4 = 13`

Now we can subtract 4 from both sides. We could also get rid of the 3/2 first, but then we'd have to worry about mixing up what to do with the 4. It's usually best to isolate "x" on one side with the rest of the numbers on the other before you do any multiplication or division:

`3/2 x = 9`

Now, things get a little tricky. If you're good with fractions, this will be no problem. If you're not great with them, we can split up this fraction into two separate operations! Look here:

`(3x)/2 = 9`

If you'll notice, we just changed the fraction expression into a multiplication step followed by a division step! Now, we can go back to "doing the opposite as what's being done to x" or however you are used to solving this. Let's start by multiplying both sides by 2:

`3x = 18`

Now, we finish up the problem by dividing by 3:

`x = 6`

And there's your answer!

If you wanted to work with fractions, we can go back to that step:

`3/2 x = 9`

We'll multiply by the reciprocal:

`2/3*3/2 x = 2/3*9`

`x = 6`

That is exactly the same thing we did before, actually, but just combined into a single step!

I hope that helps!

atyourservice's profile pic

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

Posted on


because of the minus sign in front of  (-4) the -4 becomes a positive 4


Now subtract 4

`(3/2)x =13-4`

Divide by 3/2

`((3/2)x)/(3/2) =9/((3/2)) `

x = 6

zumba96's profile pic

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

Posted on


Since there are two negatives they become positive


Move the 4 to the other side



Now multiply by the inverse to get x




jess1999's profile pic

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

Posted on

To solve for x first simply the equation.

By simplifying, your equation should look like

3/2x + 4 = 13   Now, subtract 4 from both sides

By subtracting 4 from both sides your equation should look like

3/2x = 9    Now you have to divide by 3/2 which is multiplying 9 by 2/3

By doing that you should get

x = 18/3 Now simplify

X = 6 which is your answer

micaexel's profile pic

micaexel | High School Teacher | (Level 1) eNoter

Posted on

you never want to have two minus signs next to each other. so replace them with a +...two negatives multiplied together = a positive.

then you will have 3/2x + 4 = 13

next mulitply everything by the denominator of 2 to get rid of the fraction (because most people hate fractions I always say get rid of them)

then you will have 3x + 8 = 26

next subtract 8 from both sides (inverse property)

then you will have 3x = 18

now divide both sides by 3 (inverse property)

x = 6.

check your work by substituting 6 in for x

you should always double check your work especially if taking a test or assessment, this helps a lot with multiple choice test

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