Question 1

What if you have a fraction in the equation that's like : 7/x-9 and the other side of the equation has -2/x, how would you work that out?

Accepted Answer

You will cross multiply and then solve. To cross multiply, multiply the denominator on the left by the numerator on the right. Then do the same for the denominator on the right and the numerator on the left. These new expressions will be equal to each other. For your example, it will look like:

(x-9)(-2)=(x)(7)
Distribute/multiply to get:
-2x + 18 = 7x
Add 2x to both sides to gather your variables:
18 = 9x
Divide both sides by 9.
2 = x

(x-9)(-2)=(x)(7)
Distribute/multiply to get:
-2x + 18 = 7x
Add 2x to both sides to gather your variables:
18 = 9x
Divide both sides by 9.
2 = x

Question 2

What about this equation?

```
6/x + 3 = 12/2x + 1
```

We can try to solve it as usual:

```
Let's multiply both sides on x
6 + 3x = 12/2 + x

Then isolate x (subtract it from the both sides)
6 + 2x = 12/2

This is equals
6 + 2x = 6

Subtract 6 from the both sides
2x = 0

Divide by 2 both sides
x = 0
```

But we can't substitute zero instead of `x` in the equation because it's impossible to have zero as denominator.

So should we care about exclusions for `x` when it resides in denominator?

Accepted Answer

Yes, you should care about exclusions for X.  While your work created x=0, it is not a valid solution because it doesn't make the equation be true (both sides equal).  Division by 0 is undefined.

Question 3

What if the numerator on both sides is x and the denominator of both fractions does not have a common multiple? Could we still solve for x using this method or some other type?

Accepted Answer

IDK
ask chat gpt

Question 4

Why does multiplying x by 10/x get you 10? Is it because if u multiply you get 10x over x which simplifies into 10?

Accepted Answer

Remember that "x" is really "x/1," just like 2 is 2/1.
Let's take a similar problem without variables: 2 &bull; 3/2.
When you multiply 2 (or 2/1) by 3/2, you multiply numerator by numerator, and denominator by denominator. You end up with 6/2. When you reduce (or simplify), you divide both the numerator and the denominator by their GCF (greatest common factor). 6/2 = 3, and 2/2 = 1. 
So you're left with 3/1, or *3*.

Now look back at your original problem, x &bull; 10/x. When you multiply (remember that x = x/1), you end up with 10x/x. Now we need to simplify. Obviously the only factor between the top and bottom is x, so we divide both the numerator and the denominator by x.
10x/x = 10, and x/x = 1,
so we're left with 10/1, or *10*.

Question 5

In the video, Sal minused the 2x, but couldn't you also minus the 7x to? I

Accepted Answer

Yes, you could have subtracted 7x rather than the 2x.  If you prefer to work with positive numbers, then moving the 2x keeps the coefficient of x a positive value.

Question 6

I don't get how "X ⋅ -10/X = -10"

Where'd the X go? can someone please break it down for me.

Accepted Answer

The -10/x means -10 divided by x.
 
When you multiply the whole side by x you multiply the -10 AND you multiply the "divided by x"

That would be like saying "-10 times x" ( which is the same as -10x) "divided by x times x" which when dividing and multiplying at the same time it cancels itself out so the x in the denominator goes away.

x times x divided by x is redundant so it cancels itself out.

Consider the same in addition and subtraction. 10+x-x= 10 since the plus and minus x cancel each other out. The same happens here because the times and divided by x in the denominator cancel out.

Question 7

If 19=43+X what is the value of X

Accepted Answer

The answer is negative 24, because 43+(-24)=19, or you can solve it by isolating the x, to do this, put the-equation X+43=19, subtract 43 from both sides so it will look like, (X+43)-43=(19)-43, so (x+43)-43 is X, (19)-43 is -24, so X=-24.

Hope this helps.

Hope this helps.

8th grade

Course: 8th grade > Unit 2

Equation with the variable in the denominator

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