PRACTICE
Write a system of inequalities for each graph shown.
(1)
(2)
(3)
(4)
INEQUALITIES:
INEQUALITIES:
INEQUALITIES:
INEQUALITIES:
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
PRACTICE
Graph each system of inequalities. Shade only the solution (overlapping) region.
(5) 𝑦 ≤ −𝑥 + 5
𝑦 < 3𝑥 − 4
(6) 𝑦 > −2𝑥
𝑦≤3
(7) 𝑥 > 0
𝑥≤3
Is (—1,—4) a solution?
Is (—2,0) a solution?
Is (1,6) a solution?
YES / NO
PRACTICE
YES / NO
YES / NO
Write each inequality in graphing form. Then graph and shade the solution region.
(8) 4 ≤ 𝑥 − 𝑦
(9) 6𝑦 + 5 < 4𝑦 − 1
GRAPHING FORM: __________________
GRAPHING FORM: __________________
𝑥 + 3𝑦 > 6
4(𝑥 + 1) ≤ −4
GRAPHING FORM: __________________
GRAPHING FORM: __________________
PRACTICE
(10) Students are required to burn 380 calories during a 40-minute
PE class, during which they must jog and play soccer. If a student burns 8
calories per minute playing soccer and 12 calories per minute jogging, how long
should a student spend doing each activity?
PRACTICE
(11) One sandwich and two drinks cost $6 at the cafeteria. Three
sandwiches and nine drinks cost $24. What is the price of each item?
SOCCER: ____________
JOGGING: ____________
DRINK: ____________
SANDWICH: ___________
PRACTICE
(12) An auto manufacturer makes cars and trucks in the same factory. A car requires four
seats and six cupholders. A truck requires two seats and four cupholders. The factory currently has
120 seats and 220 cupholders in stock. If c=car and t=truck, which inequalities model this scenario?
a) 4𝑐 + 6𝑡 ≤ 120
2𝑐 + 4𝑡 ≤ 220
b) 4𝑐 + 2𝑡 ≤ 120
6𝑐 + 4𝑡 ≤ 220
c) 4𝑐 + 2𝑡 ≤ 220
6𝑐 + 4𝑡 ≤ 120
d) 4𝑐 + 2𝑡 ≤ 6𝑐 + 4𝑡
𝑐 + 120 ≤ 𝑡 + 220
Solve each system of equations. Circle which method you used.
REVIEW
(13) −𝑥 + 5𝑦 = 17
2𝑥 − 10𝑦 = −34
(14) 4𝑥 + 9𝑦 = 10
−8𝑥 − 12𝑦 = −8
_________
_________
SUBST
REVIEW
/
COMBO
SUBST
Let 𝑓(𝑥) =
/
(15) 𝑥 + 𝑦 = 1
2𝑥 − 3𝑦 = 12
(16) 7𝑥 + 2𝑦 = −3
−14𝑥 − 4𝑦 = −6
_________
COMBO
SUBST
/
_________
COMBO
SUBST
/
COMBO
, 𝑔(𝑥) = −(𝑥 ), and ℎ(𝑥) = 𝑥 − 4𝑥 − 10.
(17) 𝑓(4) = ______
(18) 𝑔(−2) = ______
(19) 𝑓 𝑔(−1) = ______
(20) 𝑔 ℎ(1) = ______
(21) If 𝑓(𝑥) = ,
what was x? ______
(22) If ℎ(𝑥) = −14,
what was x? ______
(23) ℎ 𝑔(𝑥) =______________________
REVIEW
Solve each equation.
+ =
______
(26)
(28) + = −
______
(29)
(25)
REVIEW
(24) 𝑔 𝑔(𝑥) =______________________
𝑥 + 3𝑥 − =
______
− 3 = 2 ______
(27) −2 +
= 8 ______
(30) 12 − (
+ 𝑥) = 2 ______
(31) Circle the error in the solution to the equation. Then fix the error in the space below.
Solve:
Step 1:
Step 2:
Step 3:
Step 4:
CHALLENGE
CORRECT SOLUTION:
__________
Solve each compound inequality. Graph your solutions on a number line.
(32) 14 < 2𝑥 − 6 ≤ 22
(33) −3 ≤ −2𝑥 + 1 < 11