Make x the subject of 5x + c = dx + 2 Step by Step

Step by step

The question

Question: make x the subject of 5x + c = dx + 2.

5x + c = dx + 2

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

dx is on the right.

To remove it, we take away dx.

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

5x + c − dx = dx + 2 ~~− dx~~

Careful!

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

dx becomes −dx.

Careful: not 5x + c + dx = 2 ✗

dx and −dx make zero.

Cross them out.

Now we have 5x + c − dx = 2.

5x + c − dx = 2

c has no x.

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

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

5x ~~+ c~~ − dx ~~− c~~ = 2 − c

c and −c make zero.

Cross them out.

Now both x terms are on the left: 5x − dx = 2 − c.

5x − dx = 2 − c

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 (5 − d) is 2 − c.

x(5 − d) = 2 − c

3 Remove the (5 − d)

(5 − d)x means (5 − d) times x.

We want just x.

To remove times (5 − d), we divide by (5 − d).

We do it on both sides.

~~(5 − d)~~x~~(5 − d)~~ = 2 − c(5 − d)

(5 − d) divided by (5 − d) is 1.

So just x is left.

So x = (2 − c)/(5 − d).

x = 2 − c(5 − d)

4 Check

Let's check with numbers.

We pick c = 3, d = 6.

Our answer gives x = 1.

x = 2 − 35 − 6 = −1−1 = 1

Now we put all the numbers into the start.

First the left side.

Left: 5(1) − (6)(1) = 5 − 6 = −1

Now the right side.

Right: 2 − 3 = −1

Both sides are −1.

So our answer is right!

Both sides equal −1

Let's look back.

First: get the x terms on one side.

Then: take x out.

Then: remove the (5 − d).

Last: check.

Answer