Solve 2x - 1 < -5 or 2x - 1 > 3 Step by Step

Step by step

The question

Question: solve 2x − 1 < −5 or 2x − 1 > 3.

Two inequalities, joined by "or".

2x − 1 < −5 or 2x − 1 > 3

"Or" means: x can make one of them true, or the other.

We solve both, side by side.

or: one of them is true

1 Remove the − 1

We want x by itself.

The − 1 is in the way.

In each one, we add 1 on both sides.

2x ~~− 1 + 1~~ < −5 + 1 or 2x ~~− 1 + 1~~ > 3 + 1

− 1 and + 1 make zero, in both.

−5 plus 1 is −4.

3 plus 1 is 4.

−5 + 1 = −4, 3 + 1 = 4

Now we have 2x < −4 or 2x > 4.

2x < −4 or 2x > 4

2 Remove the 2

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

In each one, on both sides.

2 is a positive number, so the sign stays the same.

2x2 < −42 or 2x2 > 42

2 divided by 2 is 1.

So just x is left.

−4 divided by 2 is −2.

4 divided by 2 is 2.

−42 = −2, 42 = 2

So x < −2 or x > 2.

x < −2 or x > 2

3 Show it on a number line

Books also write the answer like this.

It is called interval notation.

A round bracket means the end is not in, like the open circle.

∞ means it goes on for ever.

∪ means or.

interval: (−∞, −2) ∪ (2, ∞)

4 Check

Let's test one number from each part.

First −3, from the left part.

x = −3: 2(−3) − 1 = −6 − 1 = −7

−7 is less than −5.

True!

−7 < −5

Now 3, from the right part.

x = 3: 2(3) − 1 = 6 − 1 = 5

5 is greater than 3.

True!

Both parts work!

5 > 3

Let's look back.

First: remove the − 1.

Then: remove the 2.

Then: show it on a number line.

Last: check.

Answer