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

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

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

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

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

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

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

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

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

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