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1. Algebra Review Problems:
(a) (3 points) Simplify:
x3 − 27
x2 − 9
4x
(b) (3 points) Simplify:
x2 − 1
−
(a)
x
x2 − x − 2
(b)
2. (4 points) Graph and shade the solution:
y < −2
y
x≥2
y
x
Page 1 of 4
Study Guide 5
x
Total Points: 50
3. (4 points) Graph and shade the solution:
−3
y<
y≥
x+3
4
x−4
3
4
y
y
x
x
4. (5 points) Graph and shade the solution to each of the system of linear inequalities:
−2
x +2
3
x ≥ −1
y ≥ −2x + 3
y <
y≤1
y
y
x
Page 2 of 4
Study Guide 5
x
Total Points: 50
5. (8 points) Graph and shade the solution to each of the system of linear inequalities:
y > 2x − 2
y ≥x−4
3
y > −2
3 x−2
y≤0
y≤2
x≥0
y
y
x
x
6. (5 points) Find a system of linear inequalities that satisfies the following shaded
region.
y
x
6.
Page 3 of 4
Study Guide 5
Total Points: 50
7. (3 points) Solve (x − 2)(x + 3) ≤ 0, graph your final answer and in interval notation.
7.
-4
-3
-2
-1
0
1
2
3
4
8. (5 points) Solve x − x ≥ 6, graph your final answer and in interval notation.
2
8.
-4
-3
-2
9. (5 points) Solve
-1
x+5
0
1
2
3
4
≥ 0, graph your final answer and in interval notation.
x2 − 4
9.
-4
-3
-2
-1
0
1
2
3
4
5
6
7
10. (5 points) Solve x −5x ≤ 4x−20, graph your final answer and in interval notation.
3
2
10.
-4
Page 4 of 4
-3
-2
-1
0
Study Guide 5
1
2
3
Total Points: 50
4
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