How are the following equations solved

Solve linear equations

Here you will learn what linear equations are and how to solve them. Let's look at this:

  • A Explanation how to solve linear equations
  • Examples for solving linear equations.
  • Tasks / exercises so that you can practice this yourself.
  • A Video for solving equations.
  • A Question and answer area to this topic.

Tip: We'll look at how to solve linear equations here. If this is not enough, you are welcome to take a look at how to solve simple equations. You can find this under Solving / rearranging equations.

Explanation of solving linear equations

What are linear equations? Let's look at a definition:

Note:

A linear equation (with one variable) is, or can be written to, an equation in the following form:

The next three equations are linear because they have the form above, or can be brought to this form:

A linear equation is solved by solving for the variable. In this case the variable is x. In the end, the equation should look like we have x = .... there. Let's look at some examples.

method:

  • Equations are solved by performing the same calculation steps on both sides of the equation.
    • If I add the number 5 on the left side, I have to do the same on the right side of the equation.
  • The calculation steps are carried out in such a way that at the end the variable x remains on one side and everything else on the other side.
Display:

Example solving linear equations

Let's look at some examples of how to solve linear equations.

example 1:

Solve the equation 4x - 8 = 0.

Solution:

To solve this equation for x, we first add +8 on both sides of the equation. As a result, the -8 disappears on the left and on the right we get 0 + 8 = 8. The respective calculation steps can be written behind a line. To solve for x we ​​have to divide the 4x by 4. This gives us 1x on the left and 8: 4 = 2 on the right. The solution to the equation is x = 2.

Example 2:

The equation 2 (x - 1) = 8 + 4: 2 is to be calculated. How big is x?

Solution:

On the left side of the equation, we first solve the bracket. To do this, we take the 2 in front of the bracket and multiply it by x. This gives us 2x. We also take the 2 in front of the bracket and multiply it by the -1 in the bracket. This equals -2. On the right side, we have to pay attention to the point before the line, so we first perform the division 4: 2 = 2. To solve for x we ​​need to eliminate the -2 on the left. For this we have to calculate +2 on both sides. We get 2x = 12. We divide both sides by 2 and get x = 6.

Tasks / exercises linear equations

Show:

Solve video equation

Solve simple equations

In the next video you will learn how to solve simple equations:

  • It explains what an equation is and how to solve it.
  • Corresponding examples are calculated for this.

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Questions with answers linear equations

In this section we look at typical questions with answers about linear equations.

Q: What other types of linear equations are there?

A: We discussed linear equations with one variable earlier. However, there are also linear equations with two variables. In school, for the most part, these equations have not just the variable x, but the variables x and y.

Q: What topics should I look at next?

A: In addition to solving linear equations - also with two variables - there are linear systems of equations. These are several equations that are related and must be solved together. Equations can also be non-linear. With a power of the second degree this is called a quadratic equation, with a power of the third degree it is called a cubic equation. In addition to equations, there are also inequalities. This content is already available: