1. Solving Equations & Inequalities Word Problems
Objectives:
To solve word problems involving linear equations and inequalities.

2. VOCAB OF WORD PROBLEMS ADDITION SUM MORE THAN PLUS INCREASED BY
SUBTRACTION
DIFFERENCE
LESS THAN
MINUS
DECREASED BY
MULTIPLICATION
PRODUCT
TIMES
MULTIPLIED BY
PER
DIVISION
QUOTIENT
DIVIDED BY

3. IS GREATER THAN OR EQUAL TO
VOCAB OF WORD PROBLEMS
WORD
OPERATION
IS/ARE =
IS LESS THAN
<
IS GREATER THAN
>
IS LESS THAN OR EQUAL TO ≤
IS GREATER THAN OR EQUAL TO ≥
QUANTITY
( )
A NUMBER X
OPPOSITE OF A NUMBER -X

4. Write & solve an inequality. Label each step (DCMAM)
1) Three times a number n decreased by two is less than or equal to five times a number n.
Move the variable to one side
M – Divide by the coefficient

5. Move the variable to one side
Write & solve an inequality. Label each step (DCMAM)
2) Three times the sum of a number x and two is less than twice a number x increased by 6.
Distribute
Move the variable to one side
A – Subtract the
constant

6. Move the variable to one side
Write & solve an inequality. Label each step (DCMAM)
3) Four times a number n decreased by 7 is greater than or equal to five times the sum of twice a number n and seven.
Distribute
Move the variable to one side
A – Subtract the
constant
M – Divide by the coefficient

7. Variable Key info Word equation Numeric equation
Write & solve an inequality.
4) A manufacturer of remote-control race cars sells them for $18 each. The cost to run the company is $2,000 per day plus $13 to build each car. What is the minimum number of cars that must be sold each day for the company to make a profit?
Variable
Let C = minimum # of cars that must be sold to make a profit
Key info
Word equation
Income > expenses
Numeric equation

8. Solve
They must sell more than 400 cars to make a profit. That means, at least 401 cars.

9. Variable Key info Word equation Numeric equation
Write & solve an inequality.
5) A store charges $4 per game to rent a video game. A club charges only $2 per game, but has a membership fee of $50 per year. At least how many games must you rent each year so that renting from the club costs less than renting from the store?
Variable
Let g = minimum # of games you need to rent each year to make renting from club less than the store
Key info
Word equation
Club cost < store cost
Numeric equation

10. Solve
You must rent more than 25 games to make the club costs less than the store cost. That means, at least 26 games.