### Solving Linear Equations - Part 2

#### Lesson Objective

This lesson shows you some examples on solving linear equations. These examples will help in your understanding on this topic.

#### About This Lesson

This lesson is a continuation from Part 1 for this topic.

After learning the basic concepts behind solving linear equations, it is time to take a look at some examples to understand these concepts better.

### Study Tips

#### Tip #1

Remember that when we solve a linear equation, whatever terms that are added to one side of the equation, the same terms must be added to the other side of the equation.

This is important to keep the equation balanced.

#### Tip #2

When we multiply both sides of the equation, it is important to multiply 'all' the terms in the equation. For example, when we multiply the following equation with 3:

2x + 1 = 4x -8

The equation becomes:

**3(**2x +1**)** = **3(**4x -8**)**

Notice that, we put brackets around all the terms to both sides of the equation. By doing so, the equation will remain balanced.

#### Tip #3

Similarly, when we divide both sides of the equation, it is important to divide all the terms in the equation. For example, when we divide the following equation with 3:

2x + 1 = 4x -8

The equation becomes:

**(**2x +1**)/3** = **(**4x -8**)/3**

Notice that, we need put brackets around all the terms to both sides of the equation. By doing so, the equation can remain balanced.

Now, watch the following math video to know more.

### Math Video

#### Video on Solving Linear Equations

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I'd like to contribute or to know more about the app#### Math Video Transcript

00:00:01.050

This lesson shows you some examples on solving linear equations.

00:00:05.230

To solve a linear equation, our objective is to find what value x is equals to.

00:00:12.080

Now, Let's solve, 2x -1 = 5 + 4x.

00:00:18.160

Since our objective is to find what is x equals to. we need to put all the terms with x, on on one side of the equation, usually, on the Left hand side.

00:00:29.050

We can do so by removing +4x. To do so, we add -4x to both sides of the equation.

00:00:41.040

The equation now becomes 2x -1 -4x = 5.

00:00:47.220

Now, notice that we also need to remove negative 1? To do so, we add +1 to both sides of the equation.

00:00:59.130

The equation becomes 2x -4x = 5 + 1.

00:01:05.110

Alright, we now add the like terms together.

00:01:09.230

Adding 2x with -4x gives -2x.

00:01:17.080

Adding 5 with 1 gives 6.

00:01:21.060

Now, notice that to find x, we need to remove -2 from -2x.

00:01:29.060

We can do so by dividing both sides of the equation by -2. So, we get x = +6/-2

00:01:43.100

Finally, we can solve for x by dividing +6 with -2. This gives x = -3.

00:01:54.090

Next example on solving linear equations, let's solve 2(2x -1) = 2x +8.

00:02:01.150

First, we need to remove the brackets.

00:02:07.180

2 multiply by 2x gives +4x. 2 multiply by -1 gives negative 2. Now, let's put these terms back into the equation.

00:02:22.220

Now, we can remove 2x by adding -2x to both sides of the equation.

00:02:31.220

This gives +4x -2 -2x = +8.

00:02:38.040

Now, we can remove -2 by adding +2, to both sides of the equation.

00:02:46.110

This gives +4x -2x = +8 + 2.

00:02:52.090

We can simply this equation by adding 4x and -2x . This gives +2x.

00:03:03.000

Now, add +8 with +2. This gives +10.

00:03:09.000

To find x, we need to remove +2 from +2x. We can do so by dividing both sides of the equation by +2.

00:03:15.010

The equation becomes x = +10/+2. Now, we divide +10 with +2. This gives 5.

00:03:33.060

So, the answer is x = 5.

00:03:38.100

Next example on solving linear equations. Let's solve. 2 (x +1) = 5 – 3(x -1).

00:03:46.100

First, we need to remove the brackets in this equation. Let's start with 2 bracket x+1.

00:03:55.000

2 multiply by x gives 2x. 2 multiply by +1 gives +2. Let's put these terms back.

00:04:07.240

Now, let's remove the brackets in -3(x -1).

00:04:15.080

-3 multiply by x gives -3x. -3 multiply by -1 gives +3. Let's put these terms back.

00:04:30.100

Now, we need to remove -3x from the Right Hand Side. To do so, we add +3x to both sides of the equation.

00:04:41.230

By doing so, the equation becomes 2x +2 +3x = 5 +3.

00:04:49.160

We can remove +2 by adding -2 to both sides of the equation. The equation now becomes 2x +3x = 5 +3 -2.

00:05:04.010

Now, we simplify the equation by adding 2x with 3x. This gives +5x

00:05:12.100

3 minus 2 gives 1. 5 plus 1 gives 6.

00:05:19.090

Now, to get x, we need to remove +5. We can do so by dividing +5 to both sides of the equation.

00:05:31.100

This gives, x = +6 / +5.

00:05:38.110

Now, since 6 divides by 5 is not an integer, we can leave the answer in the form of fraction.

00:05:45.120

So, the answer is x = 6/5.

00:05:52.140

Final example on solving linear equations, let's simplify x/4 + 2 = x -1.

00:05:59.130

Now, we can remove +2 by adding -2 to both sides of the equation.

00:06:07.010

The equation now becomes, x/4 = x -1 -2.

00:06:13.220

Now, we can add -1 and -2. This gives -3.

00:06:19.190

It is easier to solve this equation if we remove the denominator, 4, from this equation.

00:06:27.110

We can do so by multiplying both sides of the equation by 4.

00:06:33.110

The equation now becomes x = 4(x -3). Remember to put brackets around the terms when multiplying.

00:06:42.230

To proceed, we need to remove these brackets.

00:06:48.080

4 multiply by x gives 4x. 4 multiply by -3 gives -12. Let's put back these terms.

00:07:01.040

We can remove 4x by adding both sides of the equation by - 4x. This gives x -4x = -12.

00:07:12.160

Now, we can simplify the equation by adding x with -4x. This gives negative 3x.

00:07:21.230

To get what is x equals to, we need to remove -3 from -3x.

00:07:27.190

To do so, we divide both sides of the equation by -3.

00:07:35.070

The equation now becomes, x = -12/ -3.

00:07:41.060

Dividing -12 with -3 gives 4 . So, the answer is x = 4.

00:07:49.000

That is all for this lesson on on solving linear equations. Try out the practice questions to reinforce your understanding.

### Practice Questions & More

#### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on solving linear equations or pick your choice of question below.

- Question 1 on the basics on solving linear equations
- Question 2 on the basics on solving linear equations

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