1. Writing and Solving Linear Equations
Madison Houser

2. Expression vs. Equation
A linear expression is a combination of terms where the highest power of the variable is 1
3x+4
5x+9
An equation is a statement in which the value of 2 expressions are equal
3x+4 = 5x+6

3. Words that Mean “Equal”Is
Are
Was
Were
Will be
Gives
Yields
Spent
Total of
Sold for
There are other words that aren’t on here

4. Step 1: Define the Problem
Read the problem carefully
- Read a few times before you start Defining
Bennett and his friends decide to go bowling. The cost for the group is $15 for shoe rentals plus $4 per game. If they spent $47, how many games did they pay for?
Identify what you are trying to find
How many games did the group pay for?
Determine what information is available to help you find it.
$15 for shoes for the entire group
$4 per game
They spent $47

5. Step 2: Assign Variables
Choose a variable to assign to an unknown quantity in the problem.
Use g to represent the cost per game
If other unknown quantities exist, express them in terms of the selected variables.
No other unknowns

6. Step 3: Translate into an Equation
Use the relationships among the known and unknown quantities to form an equation.
Bennett and his friends decide to go bowling. The cost for the group is $15 for shoe rentals plus $4 per game. If they spent $47, how many games did they pay for?
The relationships will be referred to in terms of operations:
Addition
Subtraction
Multiplication
Division
4g + 15 = 47

7. You try!
The Ace Telephone Co. charges a flat monthly fee of $22.00 for a telephone line and $0.20 per minute for long distance calls. If you want to spend $27 for one month how many long distance minutes can you use per month?
Equation: 0.20m + 22 = 27

8. Step 4: Solve the Equation
Determine the value of the variable
4g + 15 = 47
Use the result to find any other unknown quantities in the problem.

9. Step 5: Check the Reasonableness of Your Answer
Check to see if your answer makes sense within the context of the problem.
If not, check your work for errors and try again.

10. Step 6: Answer the Question
Write a clear statement that answers the question(s) posed.
Bennett and his friends paid for 9 games of bowling.

11. You Try! Continued..
The Ace Telephone Co. charges a flat monthly fee of $22.00 for a telephone line and $0.20 per minute for long distance calls. If you want to spend $27 for one month how many long distance minutes can you use per month?
Equation: 0.20m + 22 = 27
Solution: You can use 25 long distance minutes per month.

12. Other Equations to Solve
3x + 15 = x + 25
2x + 3 = 6 – (2x – 3)