SIMPLE EQUATION

 

Welcome to class! 

In today’s class, we will be talking about a simple equation. Enjoy the class!

Simple Equation

Simple Equation classnotes.ng

  • Addition and subtraction equations:

Some equations involve only addition and/or subtraction.

Example 1:

Solve for x.

x + 8 = 12

To solve the equation x + 8 = 12, you must get x by itself on one side. Therefore, subtract 8 from both sides.

equation

To check your answer, simply plug your answer into the equation:

equation

Example 2:

Solve for y.

y – 9 = 25

To solve this equation, you must get y by itself on one side. Therefore, add 9 to both sides.

equation

To check, simply replace y with 34:

equation

Example 3:
Solve for x.
x + 15 = 6
To solve, subtract 15 from both sides.equationTo check, simply replace x with –9 :equation

Notice that in each case above, opposite operations are used; that is, if the equation has addition, you subtract from each side.

  • Multiplication and division equations:

Some equations involve only multiplication or division. This is typically when the variable is already on one side of the equation, but there is either more than one of the variable, such as 2 x, or a fraction of the variable, such as

equation or equation

In the same manner, as when you add or subtract, you can multiply or divide both sides of an equation by the same number, as long as it is not zero, and the equation will not change.

Example 4:

Solve for x.

x = 9

Divide each side of the equation by 3.

equation

To check, replace x with 3:

equation

Example 5:

Solve for y.

equation

To solve, multiply each side by 5.

equation

To check, replace y with 35:

equation

Example 6:

Solve for x.

equation

To solve, multiply each side by equation.

equation

Or, without cancelling,

equation

Notice that on the left you would normally not write equation because it would always cancel to 1x or x.

equation

  • Combinations of operations:

Sometimes you have to use more than one step to solve the equation. In most cases, do the addition or subtraction step first. Then, after you’ve sorted the variables to one side and the numbers to the other, multiply or divide to get only one of the variables (that is, a variable with no number, or 1, in front of it: x, not 2 x).

Example 7:

Solve for x.

x + 4 = 10

Subtract 4 from both sides to get 2 x by itself on one side.

equation

Then divide both sides by 2 to get x.

equation

To check, substitute your answer into the original equation:

equation

 

In our next class, we will be talking about the Geometry of Plane Shapes.  We hope you enjoyed the class.

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

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