Chapter 2 Review

Solve and Graph

100

Solve and graph: x+7≥12

x≥5 (closed circle at 5, arrow right)

200

Solve and graph: 2x−5<9

•  x<7 (open circle at 7, arrow left)

300

−3x+4≤−8

x≥4 (closed circle at 4, arrow right)

400

Solve and graph: x/4+3>7

•  x>16 (open circle at 16, arrow right)

500

Solve and graph: −5x−10≥15

x≤−5 (closed circle at -5, arrow left)

Real- World Scenarios

100

A taxi charges a $5 base fare plus $2 per mile. You have $35 to spend. Write an inequality to represent the maximum number of miles mm you can travel.

5+2m≤35 or m≤15

200

A gym membership costs $40 per month plus a $50 enrollment fee. You want to spend no more than $250. Write an inequality for the number of months nn you can afford.

50+40n≤250 or n≤5

300

A catering company charges a $120 setup fee plus $15 per person. Your budget is at most $450. How many people pp can attend?

120+15p≤450 or p≤22

400

You're buying concert tickets that cost $85 each plus a $12 service fee per ticket. You have $600. Write and solve an inequality for the number of tickets tt you can buy.

 t≤6

500

A food truck charges a $30 delivery fee, $8 per sandwich, and $4 per drink. You order the same number of sandwiches as drinks and want to spend no more than $150. Write an inequality to find how many of each item xx you can order.

x≤10

Multi-Step Inequalities

100

3x+8≤29

• 
  x≤7

200

5x−12>18

• x>6

300

 −2x+15≥3

x≤6

400

4(x−3)<20

x<8

500

−3(2x+5)≥9

x≤−4

Solution Sets

100

What values satisfy x−4<2?
Options: 3, 5, 7, 9

• 3, 5 (values less than 6)

200

Which values satisfy 2x+3≥11?
Options: 2, 3, 4, 5, 6

4, 5, 6

300

Which values satisfy −x+10≤5?
Options: 3, 4, 5, 6, 7

• 5, 6, 7 (values greater than or equal to 5)

400

Determine the solution set for 5x−20<5x+10:
No Solution, All Real Numbers, x<6, x>6

• All Real Numbers (the inequality simplifies to −20<10, which is always true)

500

Determine the solution set for 3x+7≥3x−2
No Solution, All Real Numbers, x≥3, x≤−3

All Real Numbers (the inequality simplifies to 7≥−2, which is always true)

Compound Inequalities

100

x>2 AND x<8

 2<x<8

200

Solve: −1<x+3<5

 −4<x<2

300

Solve: 4≤2x+2≤10

1≤x≤4

400

Two students solve 3<x+1<9.
Student A gets 2<x<8
Student B gets x>2 and x<8
Who is correct and why?

Both students are correct because both inequalities describe the same set of values. The compound inequality can be written as one statement or separated into two parts with "and."

500

−6≤−2x+4<8

−2<x≤5