1. Section 2.1 Linear Equations in One Variable
Integrated Math
Section 2.1
Linear Equations in One Variable

2. Definitions
Equation- sentence that has two expressions joined by an equal sign.
Solution set- set of all solutions that satisfy the equation.
Solve- find the solution set to an equation
Equivalent equations- equations that have the same solution set

3. When a value is entered into an equation, it will make a true statement or a false statement.

4. Checking a value!
#1Write the equation #2 Plug in the value #3 Do the math on both sides of the equation! True statement? Value works. False statement? Value does not work.

5. For the equation 2𝑥−5=22, is 12 a solution?
2 12 −5=22
19=22 false
12 is not a solution.

6. For the equation 3𝑥−10=5𝑥−22, is 6 a solution?
3 6 −10=5 6 −22
18−10=30−22
8=8
6 is a solution.

7. Properties of Equality
What you do to one side of the equation, you must do to the other side.
This applies to adding or multiplying.
Recall subtracting and dividing can be turned into adding and multiplying problems.

8. Make a line down from the equal sign. Now you have two sides.
Keep them equal when solving!!!

9. Crossing some lines can be highly dangerous!

10. Steps to Solve an Equation (find the variable)
Step #1 Draw a line down from the equal sign. Step #2 Eliminate all parentheses (if necessary) using distributive property Step #3 Combine (like terms) –on the same side of the line

11. Solve an equation means finding the variable.

12. Steps #2 and #3 can be summed up by saying
SIMPLIFY EACH SIDE OF THE EQUATION!

13. At this point, you should have a maximum of two terms per side.
Step #4 Use addition or subtraction to get all
the variable terms on one side and all
numbers on the other side
Step #5 Use division or multiplication to create
a coefficient of one in front of the
variable

14. The Zukowski Way

15. Solve
3 𝑥+2 +6𝑥=96
3𝑥+6+6𝑥 = Step 2
9𝑥+6 = Step 3
− −6 Step 4
9𝑥 =90
÷ ÷9 Step 5
𝑥 = 10

16. Try this equation!
2 𝑥+3 −7=5 5−𝑥 +8 𝑥+1

17. 2 𝑥+3 −7=5 5−𝑥 +8 𝑥+1 2𝑥+6−7 =25−5𝑥+8𝑥+8 2𝑥−1=3𝑥+33 −2𝑥 −2𝑥 −1=𝑥+33 −33 −33 −34 =𝑥

18. Assignment #7A
Pg. 75 #1-23 odd

19. Equations with Fractions
You can work with fractions Or
You can multiply both sides of the equation by “the magic number” that will eliminate all the fractions.

20. “The magic number” is the LCM (least common multiple) of all the denominators!

21. Now try this one!
Before you clear fractions, put all the numerators in parentheses.
𝑎−3 4 − 2𝑎− = 𝑎 − 1 6

22. # 𝑎−3 4 − 2𝑎− = 𝑎 − 1 6
12 (𝑎−3) 4 − (2𝑎−5) 2 =12 (𝑎+1) 3 − 1 6
3 𝑎−3 −6 2𝑎−5 =4 𝑎+1 −2
3𝑎−9−12𝑎+30=4𝑎+4−2
−9𝑎+21=4𝑎+2
−4𝑎 −4𝑎
−13𝑎+21=
− −21
−13𝑎 = −19
÷− ÷−13
𝑎 =

23. Special Cases
Sometimes the variable completely disappears when solving.
If this results in a false statement,
the solution is ∅.
If this results in a true statement,
The solution is Ɍ

24. Solve for x.
4 𝑥−2 +12=2 2𝑥−9
4𝑥−8+12=4𝑥−18
4𝑥+4 =4𝑥−18
−4𝑥 −4𝑥
4= − False
Answer ∅

25. Words you might see
Identity- an equation that has all real numbers as solutions
Conditional equation- an equation that has a solution but not all real numbers
Inconsistent equation- an equation that has no solutions

26. Successful solving Be very neat! Show all work! Write a complete
equation on each line!
Work down your paper!

27. This is the pattern! Simplify then Do something, do something
Write a new equation
… until the variable is all by itself!

28. Always write the whole equation!
NO SCRAPS!