Solve 4/x + 2 = 6 Easy

The question

Question: solve 4/x + 2 = 6.

First: a bottom can never be 0.

x at the bottom can't be 0.

So x ≠ 0.

1 Remove the fractions

The bottom is x.

Times x will remove it.

We multiply every part by x.

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

x divided by x is 1.

x times 2 is 2x.

x times 6 is 6x.

Write what is left.

No more fractions!

2 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the 2x from the left side.

To remove 2x, we take away 2x.

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

+ 2x and − 2x make zero.

Cross them out.

6x − 2x = 4x.

Now we have 4 = 4x.

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

3 Remove the 4

4x means 4 times x.

We want just x.

To remove times 4, we divide by 4.

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

4 divided by 4 is 1.

So just x is left.

4 divided by 4 is 1.

So x = 1!

4 Check

Let's check: put 1 in place of x.

First the left side.

Now the right side.

Both sides are 6.

So x = 1 is right!

Let's look back.

First: remove the fractions.

Then: get x on one side.

Then: remove the 4.

Last: check.

▶ Watch it solved

Solve 5/x - 1/2 = 2/x Medium

The question

Question: solve 5/x − 1/2 = 2 over x.

First: a bottom can never be 0.

x at the bottom can't be 0.

So x ≠ 0.

1 Remove the fractions

The bottoms are x and 2.

2x can be divided by all of them.

We multiply every part by 2x.

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

2x divided by x is 2.

2x divided by 2 is x.

2x divided by x is 2.

Write what is left.

No more fractions!

2 Remove the 10

We want x by itself.

The 10 is in the way.

To remove 10, we take away 10.

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

10 and − 10 make zero.

Cross them out.

4 − 10 = −6.

Now we have −x = −6.

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.

−1 divided by −1 is 1.

So just x is left.

−6 divided by −1 is 6.

So x = 6!

4 Check

Let's check: put 6 in place of x.

First the left side.

Now the right side.

Both sides are 1/3.

So x = 6 is right!

Let's look back.

First: remove the fractions.

Then: remove the 10.

Then: remove the −1.

Last: check.

▶ Watch it solved

Solve x/(x + 2) + 1 = 6/(x + 2) Harder

The question

Question: solve x/(x + 2) + 1 = 6/(x + 2).

First: a bottom can never be 0.

x = −2 makes x + 2 0.

So x ≠ −2.

1 Remove the fractions

The bottom is (x + 2).

Times (x + 2) will remove it.

We multiply every part by (x + 2).

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

(x + 2) divided by (x + 2) is 1.

(x + 2) times 1 is (x + 2).

(x + 2) divided by (x + 2) is 1.

Write what is left.

No more fractions!

2 Open the brackets

A bracket with a plus or nothing in front can just be removed.

3 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x terms go together.

x + x = 2x.

Now we have 2x + 2 = 6.

We want x by itself.

Two things are stuck to x: times 2 and + 2.

The + 2 is on the outside, so it comes off first.

Then the times 2.

4 Remove the + 2

To remove + 2, we take away 2.

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

+ 2 and − 2 make zero.

Cross them out.

6 − 2 = 4.

Now we have 2x = 4.

5 Remove the 2

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

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

2 divided by 2 is 1.

So just x is left.

4 divided by 2 is 2.

So x = 2!

6 Check

Let's check: put 2 in place of x.

First the left side.

Now the right side.

Both sides are 3/2.

So x = 2 is right!

Let's look back.

First: remove the fractions.

Then: open the brackets.

Then: group like terms.

Then: remove the + 2.

Then: remove the 2.

Last: check.

▶ Watch it solved