Make x the subject of 3x + a = bx Step by Step

Step by step

The question

Question: make x the subject of 3x + a = bx.

3x + a = bx

The subject is the letter on its own: we want x = ...

Here x is in two places, so we must bring them together.

1 Get the x terms on one side

bx is on the right.

To remove it, we take away bx.

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

3x + a − bx = ~~bx − bx~~

Careful!

A term that moves to the other side changes its sign.

bx becomes −bx.

Careful: not 3x + a + bx = 0 ✗

bx and −bx make zero.

Cross them out.

Now we have 3x + a − bx = 0.

3x + a − bx = 0

a has no x.

To remove it from the left, we take away a.

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

3x ~~+ a~~ − bx ~~− a~~ = 0 − a

a and −a make zero.

Cross them out.

Now both x terms are on the left: 3x − bx = −a.

3x − bx = −a

2 Take x out

x is in every part.

So we take it out once, and write what is left in a bracket.

ab + ac = a(b + c)

So x times (3 − b) is −a.

x(3 − b) = −a

3 Remove the (3 − b)

(3 − b)x means (3 − b) times x.

We want just x.

To remove times (3 − b), we divide by (3 − b).

We do it on both sides.

~~(3 − b)~~x~~(3 − b)~~ = −a(3 − b)

(3 − b) divided by (3 − b) is 1.

So just x is left.

So x = −a/(3 − b).

x = −a(3 − b)

4 Check

Let's check with numbers.

We pick a = 2, b = 4.

Our answer gives x = 2.

x = −23 − 4 = −2−1 = 2

Now we put all the numbers into the start.

First the left side.

Left: 3(2) − (4)(2) = 6 − 8 = −2

Now the right side.

Right: −2

Both sides are −2.

So our answer is right!

Both sides equal −2

Let's look back.

First: get the x terms on one side.

Then: take x out.

Then: remove the (3 − b).

Last: check.

Answer