Solving 1-step Equations

YOU MUST SHOW ALL STEPS!

What is an equation? What is a variable?

An EQUATION says that two things are equal. It will have an equals sign: 7 + 2 = 10 − 1


That equation says: what is on the left (7 + 2) is equal to what is on the right (10 − 1)

So an equation is like a statement "this equals that".


A VARIABLE is a symbol for a number we don't know yet. It is usually a letter like x or y, but it can be any letter.

The GOAL

The goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The second goal is to have the number in front of the variable equal to one.


The most important thing to remember in solving a linear equation is that whatever operation you do to one side of the equation, you MUST do to the other side. So if you subtract a number from one side, you MUST subtract the same value from the other side. You will see how this works in the examples.


The best thing about working equations is that you can check your answer each time to see if it is correct. Substitute your answer in for the variable, and solve. Do both sides of your equation match? Then you have correctly solved your equation!

Remember: We must UNDO, or do the OPPOSITE operation to solve equations.

Video Lesson

Watch the videos, Adding and Subtracting, and complete video notes in your packet.

Addition & Subtraction Examples

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ADDITION

Read the math equation from above, "y plus 14 equals 20". To get the variable alone, we must do the opposite, or subtract 14. If we subtract 14 from the left side of the equation, we MUST also subtract 14 from the right side. See the picture to see EXACTLY how work must be shown.


Don't forget to CHECK your work. To check this answer, substitute 6 in for the y.


6 + 14 = 20

20 = 20 CORRECT!

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Subtraction Example

Read the math equation from above, "x minus one hundred twenty equals eighty". To get the variable alone, we will have to ADD 120. If we add 120 to one side of the equation, we MUST add 120 to the other side of the equation. See the picture above to show EXACTLY how work must be shown.


Don't forget to CHECK your work. To check this answer, substitute 200 in for the x.


200 - 120 = 80

80 = 80 CORRECT!

COMPLETE PRACTICE PROBLEMS IN YOUR PACKET!

Video Lesson

Watch the videos, Multiplying and Dividing, and complete video notes in your packet.

Multiplication & Division Examples

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MULTIPLICATION

Read the equation from above, "3 times n equals 12". To get the variable alone, we must do the opposite of times, which is divide. If we divide 3n by 3, we must do the same to the other side, which is divide 12 by 3. See above example to show EXACT steps which must be shown.


Don't forget to check your work. To check, substitute 4 in for n:


3(4) = 12

12 = 12 CORRECT!

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DIVISION

Read the equation from above, "k divided by 2 equals 16". To get the variable alone, we must do the opposite of divide, which is multiply. We multiply by the reciprocal (make it a fraction and flip it upside down). If we multiply by 2/1 on the left side, we must do the same on the right side of the equals sign. See above example to show EXACT steps which must be shown.


Don't forget to check your work. To check, substitute 32 in for k:


32 = 16

2


16 = 16 CORRECT!

COMPLETE PRACTICE PROBLEMS IN YOUR PACKET!