Linear Equations
Solving More Complex Linear Equations
To solve a complex linear equation, we have to get all the unknowns (letter) to one side of the equal sign and the numbers to the other as we have done in the example on the right. To do this, we must perform a series of operations. You always have to apply every operation to both sides of the equal sign. In the example we have started off by removing the x on one side by subtracting x from both sides. Then we have put all numbers to one side by subtracting 10. Lastly, we divided by 3 to see what (1)x is equal to. The linear equation is now solved.
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Example 2
To solve the linear equation, we have put all unknowns on
one side and all numbers on the other side of the equal
sign. This enabled us to find the solution.
Example 1
To solve the linear equation, we have put all unknowns on
one side and all numbers on the other side of the equal
sign. This allowed us to get the solution.
The most important thing to remember is that you must always apply the operation to both sides of the equal sign. Otherwise your answer will be
incorrect.
Simplify Algebraic Expressions
We recommend that you try to simplify algebraic expressions next as this is another important skill. If you want to look for other topics, visit our library. Please share this page if you like it or found it helpful!Solving Simple Linear Equations
Linear Equations are equations with one equal sign that only include one unknown. 1 + x = x - 2 is an example of a linear equation. They are usually quite easy to solve. Simple linear equations usually have an unknown value such as x and a number on one side of the equal sign and another number one the other side. To solve these equations, we have to find the value of x by either looking at the expression or if the equation is more difficult by doing the reverse operation.
Example 1
To solve the linear equation, we have don the reverse
operation which is 9-4. This gave us the value of x which is
5.
Example 2
To solve the linear equation, we have don the reverse
operation which is 14+20. This gave us the value of x which
is 34.
Simple linear equations are very easy to solve. usually, you can just tell what the solution is and otherwise, you simply have to do the reverse operation.
If you end up with 2x or a different x value that is not just x (1x) then you have to divide both sides to find the value of x. Things get a bit more difficult
when there are two numbers or letters on each side of the equal sign.
Equations with Fractions
In some cases, you may have a fraction in a linear equation. For example, in the problem on the right. We need to remove this fraction so that we can solve the equation. To do this, just multiply both sides by the denominator of the fraction (in this case 2). This will allow us to get rid of the fraction leaving just the original numerator. Now we can solve the equation like any other linear equation.
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Chapter 12.0: Learning Outcomes
Students will be introduced to the concept of linear equations!
Students will learn how to solve simple and complex linear equations!
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