Unit 2

Writing Equation

100

 Ava has $120 saved and adds $15 each week. Noah has $180 saved and adds $10 each week.

Question: Write an equation to find the number of weeks, w, until Ava and Noah have the same amount saved.

120 + 15w = 180 + 10w

200

Jasmine has $150 saved and gets $25 each week from her job. Leo has $300 saved and loses $10 each week from buying candy.

Question: Write an equation to find the number of weeks, w, until Jasmine and Leo have the same amount saved.

150 + 25w = 300 - 10w

300

Elena started with 20 cookies and gave away x cookies. Carlos started with 30 cookies and gave away twice as many cookies as Elena did.

20 −x = 30 − 2x

Writing Inequalities

100

Gym A charges a $25 sign-up fee and $20 per month. Gym B charges a $40 sign-up fee and $18 per month.

Question: Write an inequality to find when Gym A will cost less than Gym B.

25 + 20m < 40 + 18m

200

 Gym A charges a $25 sign-up fee and $20 per month. Gym B charges a $40 sign-up fee and $18 per month.

Question: Write an inequality to find when Gym A will cost more than Gym B. 

25 + 20m > 40 + 18m

300

RideShare A charges $5 for a ride plus $1.75 per mile. RideShare B charges $3 for a ride plus $2.00 per mile.

Question: Write an inequality to find when RideShare A will cost less than RideShare B.

5 + 1.75m < 3+ 2.00m

Solving Equations

100

2x + 3 = x + 7

x = 4

200

5x - 2 = 3x + 6

x = 4

300

3x + 2 = 2x + 5  

x = 3

Solving Inequalities

100

x + 4 > 2x - 1  

x < 5

200

3x - 5 ≤ 2x + 1

x ≤ 6

300

4(x−2) > 2x + 3

x > 5.5

Miscellaneous

100

What’s the difference between an equation and an inequality?  

An equation shows equality (Example: x = 5), while an inequality shows a range of values (Example: x > 5).

200

When do you flip the inequality sign?  

Flip the sign when multiplying or dividing both sides by a negative number.

300

Explain how to check your solution for an equation.  

You re-write your equation, then plug in your solution to make sure it gives you a true statement.