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Date: _________________!
Review for Quest
Chapter 3: Inequalities (3.1, 3.2, 3.3)!
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No Calculators allowed, except on question #9!
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Solve each inequality and graph its solution.!
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1. x − 3 < 10 !!
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2 − x 8 − 3x
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5. ! 3x − x − 2 ≥ 0 !
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2. −2x + 8 ≥ 12 !
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4. 2 ≤ 3x − 7 ≤ 5 !
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6. ! x 4 − 10x 2 − 24 > 0 !
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8. ! 2x 2 + 6x < 0 !
7. ! ( x − 3) ( 2x + 3) ≤ 0 !
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Solve each inequality and graph its solution.!
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9.!
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10.!
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x 4 − 8x 2 + 6 < 0 !
f (x) ≤ 0!
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(do this one with calculator if you want)!!
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given the graph of f (x) below:!
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b. !
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11. # x 3 − 2x 2 − 5x > −6 !
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(Hint: if this does not factor by grouping, guess a root !
and use synthetic; there's an easy one) #
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12. # x 3 − 1x 2 − 9x + 9 ≤ 0 !
Graph each inequality by shading the appropriate region.!
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13.
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y ≤ −x 2 + 6x − 5 ! !
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y-intercept:! !
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vertex:!
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x-intercepts (or say “none”):!
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15.
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y > x 2 − 4x + 8 !
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14.!
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y-intercept:!
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vertex:!
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x-intercepts (or say “none”):!
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Graph the solution set of the given system of inequalities.!
y ≤ 2x + 5
x ≥ −1
x 2 + 2x + y 2 − 6y + 6 ≤ 0
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Also, find ALL points of intersection!!
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16. A rhombus has vertices (+ 5, 0) and (0, + 7). Give a system of inequalities that
describes the region bounded by the rhombus. !
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17. Graph the solution set of the given system of inequalities.
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x > y 2 − 8y + 12
( x − 2 )2 + y 2 < 25 !
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18. Solve each inequality and graph its solution.!
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x 2 − 6x + 5
≤0
a. 2
x + 2x − 35
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x 2 − 3x
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b.
x−6
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19. Which of the following is the solution set of: 3x − x − 2 ≥ 0 !
a. !
2
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b.!
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c.!
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d.!
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20.
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1
2
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e.
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Write an inequality for the graph below. Assume a dotted boundary. !
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21. Graph the solution set of the given system of inequalities.!
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y ≤ −x 2 + 2x + 4 !
9 ( x − 1) + 4 ( y − 3) ≤ 36 !
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22. Solve each inequality. Show a number line and a solution using interval notation.!
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a.
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c.
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e.
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( x + 1)( x − 4 )2
( x + 5 )2
>0 !
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x 2 − 8x + 15
≤ 0!
b.
( x − 5 )2
x 4 − 3x 2 − 10 > 0 ! !
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d. x 3 + 2x 2 − 11x + 12 < 0 !
(! x + 3)2 ( x − 2 ) ≤ 0 !
( x − 4 )( x − 2 )