Math  /  Algebra

Question8+x2=10\frac{-8+x}{2}=10

Studdy Solution

STEP 1

What is this asking? This problem is asking us to find the mystery number xx that makes the equation 8+x2=10\frac{-8+x}{2}=10 true! Watch out! Don't forget that the entire numerator, 8+x-8 + x, is being divided by 22.
It's easy to accidentally only divide the xx or the 88 by 22, but we need to divide the *whole* thing!

STEP 2

1. Isolate the xx term
2. Solve for xx

STEP 3

We want to get xx by itself, so let's **multiply both sides** of the equation by **2**.
Why? Because multiplying by **2** undoes the division by **2** on the left side.
It's like we're dividing to one! 8+x22=102 \frac{-8+x}{2} \cdot 2 = 10 \cdot 2

STEP 4

Now, we simplify!
On the left side, the **2**s divide to one, leaving us with just 8+x-8 + x.
On the right side, 10210 \cdot 2 is **20**. 8+x=20 -8 + x = 20 See how much closer we are to getting xx all alone?

STEP 5

We're *so* close!
Now, we want to get rid of that 8-8 that's hanging out with xx.
We can do this by **adding 8 to both sides** of the equation.
Remember, what we do to one side, we *must* do to the other!
Adding to zero is the name of the game! 8+x+8=20+8 -8 + x + 8 = 20 + 8

STEP 6

On the left side, 8-8 and 88 add to zero, leaving just xx.
On the right side, 20+820 + 8 is **28**. x=28 x = 28 We did it!
We found the mystery number!

STEP 7

The value of xx that makes the equation true is x=28x = 28.

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