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How to solve Linear Equations?

Level 1: Linear equations of the form ax = b

Level 2: Linear equations of the form ax + b = c

Level 3: Linear equations with multiple variables and constant terms

Level 4: Linear equations with variable expressions in the denominator of fractions

An **equation** shows a relationship between two quantities that are of the same value. The symbol for equality is ‘=’.

An equation consists of a left hand side (LHS) and a right hand side (RHS). Both the LHS and RHS have the same value.

In order to preserve the equality of the equation, whatever operations performed to the LHS must also be performed to the RHS.

* Example* :

10 + 5 = 15

10 + 5 - 7 = 15 - 7 (Subtract 7 from both sides of the equation)

An equation can also contain variables.

* Example* :

x– 4 = 6

To solve the equation means that we need to look for a value for the variable that would make the equation true.

In this case, the value of *x* = 10 would certainly make the above equation true. In mathematics, we say that *x* = 10 **satisfies** the equation.

One method to solve an equation would be to **separate the unknown from known values**. We move or keep the unknown on the left-hand side (LHS) of the equation and the known values on the right-hand side (RHS) of the equation like this:

To do so, we need to perform some operations on both sides of the equation.

The following videos will show four types of linear equations and how to solve each type.

**Level 1: Linear equations of the form ax = b**

**Level 2: Linear equations of the form ax + b = c**

**Level 3: Linear equations with multiple variables and constant terms **

**Level 4: Linear equations with variable expressions in the denominator of fractions. **

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.