Solve 10 = 3 - x/2 Step by Step

Step by step

The question

Question: solve 10 = 3 − x/2.

10 = 3 − x2

1 Remove the fraction

The bottom number is 2.

Times 2 will remove it.

We multiply every part by 2.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

2 × 10 = 2 × 3 − ~~2 ×~~ x2

2 divided by 2 is 1.

Write what is left.

2 × 10 = 2 × 3 − x

Do the multiplications.

No more fractions!

20 = 6 − x

Let's swap the two sides, so x is on the left.

6 − x = 20

2 Remove the 6

We want x by itself.

The 6 is in the way.

To remove 6, we take away 6.

We do it on both sides, so they stay equal.

6 − x ~~− 6~~ = 20 − 6

6 and − 6 make zero.

Cross them out.

20 − 6 = 14.

20 − 6 = 14

Now we have −x = 14.

−x = 14

3 Remove the −1

−x means −1 times x.

We want just x.

To remove times −1, we divide by −1.

We do it on both sides, so they stay equal.

−x−1 = 14−1

−1 divided by −1 is 1.

So just x is left.

14 divided by −1 is −14.

14−1 = −14

So x = −14!

x = −14

4 Check

Let's check: put −14 in place of x.

First the left side.

Left: 10

Now the right side.

Right: 3 − (−14)2 = 3 + 7 = 10

Both sides are 10.

So x = −14 is right!

Both sides equal 10

Let's look back.

First: remove the fraction.

Then: remove the 6.

Then: remove the −1.

Last: check.

Answer