Graded Assignment
MTH303A/MTH304A: Algebra II | Unit 4 | Lesson 10: Inequalities Unit Test
Name:
Date:
Graded Assignment
Unit Test, Part 2: Inequalities
Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for
full credit.
(5 points)
1. Solve the inequality 4x  10  14 . Write the solution in interval notation and graph the
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solution set on the number line. Show all your work.
Answer:
l4x – 10l (>=) 14
l4x – 10 + 10l (>=) 14 + 10
l4xl (>=) 24
4x / 4 (>=) 24/ 4
X (>=) 6
[6, infi)
l4x – 10l (<=) -14
l4x – 10 + 10l (<=) -14 + 10
l4x l (<=) -4
4x / 4 (<=) -4 / 4
X (<=) -1
(-infi, -1]
Solution in interval notation: (-infi, -1] U [6, infi)
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Graded Assignment
MTH303A/MTH304A: Algebra II | Unit 4 | Lesson 10: Inequalities Unit Test
(5 points)
2. Graph the inequality y  3 x  4 . Show all your work.
2
Score
Answer:
Slope: 3/2: up 3 over 2
Y intercept: -4
Y < 3/2 – 4 because of the < sign the line is dotted (could not get a dotted line) and the region below the
boundary line ( y < 3/2 – 4)
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Graded Assignment
MTH303A/MTH304A: Algebra II | Unit 4 | Lesson 10: Inequalities Unit Test
(10 points)
3. Graph the system of inequalities. Clearly label the boundary lines. Then use your graph to
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identify any two points that are solutions to the system. Show and explain your work.
 y  1 x  2
4

 x  y  3
Answer:
Shaded
region
1:
Y > 1/4x – 2 (note this is a dotted line could not make a dotted line)
2:
X + y (<=) 3x
X - X + y (<=) 3 – x
Y=3-x
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Graded Assignment
MTH303A/MTH304A: Algebra II | Unit 4 | Lesson 10: Inequalities Unit Test
Solution Point 1:
(1,-1)
Y> 1/4x – 2
-1 > ¼ x 1 – 2
-1 > 1/4 – 2
-1 > -1 ¾ (true)
X + Y (<=) 3
1 + -1 (<=) 3
0 (<=) 3 (true)
Solution Point 2:
(1,2)
Y> 1/4x – 2
2>¼x1–2
2 > 1/4 – 2
2 > -1 ¾ (true)
X + Y (<=) 3
1 + 2 (<=) 3
3 (<=) 3 (true)
Your Score
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