Unit 5 Equations & Inequalities

Solve Equations

100

x - 24 = 36

x = 60

200

x + 12 = -10

x = -22

300

x / 4 = 12

x = 48

400

2/3x = 6 

x = 9

500

5x + 6 = 31

x = 5

Solve 1 step Inequality

100

x + 6 < 4

x < -2

200

x - 4 > 12

x > 16

300

-3x > 27 

x < -9

400

x / 4 > -6

x > -24 

500

1/4x = 4 

x = 16 

Solve 2 step inequality

100

2x + 6 > -2

x > -4 

200

8x - 2 < 30

x < 4

300

x / 3 + 6 > 14

x > 24

400

-2x + 2 > -16

x < 9

500

1/2x + 3 > 9

x > 12 

Vocabulary

100

Define variable 

A symbol, typically a letter to represent an unknown number

200

Define Coefficient 

A number attached to a variable through multiplication in an algebraic expression (ex: 4x)

300

Define Isolate

To manipulate an equation / inequality so that a specific variable is completely alone on one side of the equation / inequality

400

Define Constant 

A fixed value, number on its own

500

List 2 differences between an equation and an inequality

- inequalities use inequality symbols, equations use equal sign

- Inequalities solution is a range of numbers, equations have a single solution

- When dividing or multiplying an inequality symbol will flip, an equal sign is not impacting by multiplying or dividing by a negative

Write Equation/Inequality from word problem

100

A submarine is descending at a constant rate of 12 feet per minute. After some time, the submarine has descended a total of 48 feet.

How many minutes, x, has the submarine been descending?

Write and Equation to represent this situation

-4x = -48

200

Jasmine is buying some notebooks. Each notebook costs $3. She also buys a pack of pens for $6.25. If she spends a total of $48, how many notebooks did she buy? Write an equation to represent this situaiton. 

3x + 6.25 = 48

300

A student is earning points by completing practice problems. Each set of problems is worth 6 points. The student wants to earn more than 24 points.

How many sets of problems, x, does the student need to complete to reach their goal?

Write an inequality to represent the situation. 

6x > 24

400

A student is saving money. Each week, they save $3. They already have $2 saved. The student wants to have more than $17 in total.

How many weeks, x, does the student need to save to reach their goal?

Write an inequality to represent the situation. 

3x + 2 > 17

500

A scuba diver is descending deeper underwater. The diver goes down 5 feet every minute, and they started 6 feet below the surface. The diver wants to be at a depth that is less than -21 feet.

How many minutes, x, must the diver descend to reach this depth?

Write an inequality to represent the situation. 

-5x - 6 < -21