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

Expert Answers

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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!

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