Solve (3x - 1)/4 = (x + 3)/2 Step by Step

Step by step

The question

Question: solve (3x − 1)/4 = (x + 3)/2.

Two fractions are equal.

3x − 14 = x + 32

1 Cross multiply

When two fractions are equal, we can cross multiply.

These two are equal.

(3x − 1) × 2 = (x + 3) × 4

Work out the multiplications.

2(3x − 1) = 4(x + 3)

2 Open the brackets

What is in front of a bracket multiplies every part inside.

So we write each part times what is in front.

2 × 3x + 2 × (−1) = 4 × x + 4 × 3

Work out each multiplication.

6x − 2 = 4x + 12

3 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the 4x from the right side.

To remove 4x, we take away 4x.

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.

6x − 2 − 4x = 4x + 12 ~~− 4x~~

4x and − 4x make zero.

Cross them out.

6x − 4x = 2x.

6x − 4x = 2x

Now we have 2x − 2 = 12.

2x − 2 = 12

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 add 2.

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

2x ~~− 2 + 2~~ = 12 + 2

− 2 and + 2 make zero.

Cross them out.

12 + 2 = 14.

12 + 2 = 14

Now we have 2x = 14.

2x = 14

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.

2x2 = 142

2 divided by 2 is 1.

So just x is left.

14 divided by 2 is 7.

142 = 7

So x = 7!

x = 7

6 Check

Let's check: put 7 in place of x.

First the left side.

Left: 3(7) − 14 = 21 − 14 = 204 = 5

Now the right side.

Right: 7 + 32 = 102 = 5

Both sides are 5.

So x = 7 is right!

Both sides equal 5

Let's look back.

First: cross multiply.

Then: open the brackets.

Then: get x on one side.

Then: remove the − 2.

Then: remove the 2.

Last: check.

Answer