Warm Up. 1.5 Solving Inequalities Solving How to Solve Solving inequalities is just like solving...

Warm UpWrite as an algebraic expression.1. the product of 12 and the sum of a number and 5

Solve. 2.

3.

4.

This symbol: is read as…

is read as…

is read as…

is read as…

1.5 Solving Inequalities

SolvingOur goal is to have the variable on its own on the left of the inequality sign. Like this…

How to SolveSolving inequalities is just like solving equations.

One extra detail to pay attention to is the direction of the inequality.¿BIGsmall

Safe Things to DoThese are things you can do without affecting the direction of the inequality.o Add or subtract a number from both

sideso Multiply or divide both sides by a

positive numbero Simplify a side

Changing DirectionBUT these things will change the direction of the inequality.

o Multiply or divide both sides by a negative number

o Swapping left and right hand sides.

Changing DirectionChanging direction means…

would become

would become

would become

would become

Solving Inequalities1. Get the variable on its own on

the left of the inequality sign.

2. Graph the inequality on a number line.o Open circle: and ● Closed circle: and → Arrow pointing right: and ← Arrow pointing left: and

ExamplesSolve each inequality. Then graph the solution set on a number line.

1.

2.

ExamplesSolve each inequality. Then graph the solution set on a number line.1. 2. 3.

You Try!Solve each inequality. Then graph the solution set on a number line.

1.

2.

You Try!Solve each inequality. Then graph the solution set on a number line.

1.

2.

Word Problems1. An adult panda bear (P) will

eat at least 20 pounds of bamboo every day. Write an inequality that expresses this situation.

Word Problem2. On a Ferris wheel at a carnival, only two

people per car are allowed. The two people together cannot weigh more than 300 pounds. Ron and his father want to go on the ride together. Ron’s father weighs 175 pounds.

a) Write an inequality that expresses this situation. b) Draw a visual representation on a number line, and c) Solve the inequality to find the maximum weight

Ron () can be for the two to be allowed on the ride?

Word Problem3. Rosa’s cell phone plan costs her $50 per

month plus $0.25 for each minute she goes beyond her free minutes. How many minutes () can she go beyond her free minutes and still pay less than a total of $70?

a) Write an inequality that expresses this situation.

b) Draw a visual representation on a number line, and

c) Solve the inequality.

Ticket Out The Door1. Write an absolute value equation that

corresponds to…

2. Draw a visual representation on a number line, and

3. Solve the inequality.

Tara is delivering bags of mulch. Each bag weighs 48 lbs., and the push cart weighs 65 pounds. If her flat-bed truck is capable of hauling 2000 lbs., how many bags of mulch () can Tara safely take on each trip?

HomeworkLesson 1.5Pg. 37 #’s 10-21