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$100 $100 $100 $100 $100
$200
$300
$400
$500
$200 $200 $200 $200
$300 $300 $300 $300
$400 $400 $400 $400
$500 $500$500 $500
Graphing Inequalities
One Step Inequalities
Absolute Value
Multi-Step Inequalities
Compound Inequalities
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Graphing Inequalities for $100
Graph the inequality shown below:
x > -4
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Answer
Back
X > -4
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Graphing Inequalities for $200
Write an inequality for the graph shown below:
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Graphing Inequalities for $300
Graph the inequality shown below:
-7 < x
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Answer
Back
-7 < x
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Graphing Inequalities for $400
Graph the inequality shown below:
0 ≤ x < 4
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Answer
Back
0 ≤ x < 4
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Graphing Inequalities for $500
Graph the inequality shown below. Check your answer:
x < -5 or x ≥ 2
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Answer
Back
x < -5 or x ≥ 2
Let x = -7 Let x = -4 Let x = 5
-7 < -5 =>True -4 < - 5 => NOT True 5 < -5 => NOT True
-7 ≥ 2 =>NOT True -4 ≥ 2 => NOT True 5 ≥ 2 => True
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One-Step Inequalities for $100
Solve for x:
X + 2 < 1
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Answer
X + 2 < 1 -2 -2X < -1
Back
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One-Step Inequalities for $200
Solve for x:
x/(-5) > 7
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Answer
x/(-5) > 7
x/(-5) * (-5) > 7 * (-5)
X < -35
Back
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One-Step Inequalities for $300
Solve for x:
4x ≥ -36
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Answer
4x ≥ -36
(4x)/(4) ≥ (-36)/(4)
x ≥ -9
Back
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One-Step Inequalities for $400
Write the following inequality in words:
x + 5 ≥ 7
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Answer
Back
x + 5 ≥ 7
Five more than a number, x, is greater than or equal to 7
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One-Step Inequalities for $500
Write an Inequality to model the following situation:
Mr. Sam spent at least 4 hours making this game
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Answer
Back
Let t = the time Mr. Sam spent making this game
Then,
t ≥ 4 hours
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Multi-Step Inequalities for $100
Solve for x:
x/(3) + 3 > 5
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Answer
x/(3) + 3 > 5x/(3) + 3 - 3 > 5 - 3x/(3) > 2x/(3) * 3 > 2 * 3X > 6
Back
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Multi-Step Inequalities for $200
Solve for x:
-5x + 20 ≤ 10
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Answer
-5x + 20 ≤ 10 -20 -20-5x ≤ -10(-5x)/(-5)≤ (-10)/(-5)X ≥ 2
Back
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Multi-Step Inequalities for $300
Replace the with a number that makes the inequalities equivalent
-3x >
x < -9
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Answer
-3x > (-3x)/(-3) > / (-3)x < /(-3) and x < -9So, /(-3) = -9 /(-3) * -3 = -9 * -3 = 27
Back
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Multi-Step Inequalities for $400
Solve for x:
-(x-6) + 5 - 2x < 8
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Answer-(x-6) + 5 - 2x < 8-(x-6) + 5 - 5 - 2x < 8 – 5-(x-6) - 2x < 3-x + 6 – 2x < 3-3x + 6 < 3-3x + 6 – 6 < 3 – 6-3x < -3(-3x)/(-3) < (-3)/(-3)X > 1
Back
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Multi-Step Inequalities for $500
Solve for x. CHECK YOUR ANSWER
10x – 5 - 3x > 3 – (5 - x)
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Answer10x – 5 - 3x > 3 – (5 - x)7x – 5 > 3 – 5 + x7x – 5 > -2 + x7x > 3 + x6x > 3x > 0.5
Back
Check 1: (Substitute it in –> Should be equal)
10(0.5) – 5 – 3(0.5) = 3 – (5 – (0.5))
5 - 5 – 1.5 = 3 - 4.5
-1.5 = -1.5
Check 2: (Pick value that is true)
Let x = 1
10(1) – 5 – 3(1) > 3 – (5 – (1))
10 - 5 – 3 > 3 - 4
2 > -1 => True
Check 3: (Pick value that is false)
Let x = 0
10(0) – 5 – 3(0) = 3 – (5 – (0))
-5 > 3 - 5
-5 > -2 => FALSE
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Compound Inequalities for $100
Write a compound inequality that models the graph:
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Answer
X < -3 or X ≥ -1
Back
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Compound Inequalities for $200
Solve the following inequality:
|-2(3-x) +2| -1 > 11
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Answer|-2(3-x) +2| -1 > 11|-2(3-x) +2| -1 + 1 > 11 + 1|-2(3-x) +2| > 12|-6+2x +2| > 12|2x -4| > 122x -4 > 12 or 2x -4 < -122x > 16 or 2x < -8x > 8 or x < -4
Back
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Compound Inequalities for $300
Solve the following inequality:
1 ≤ -2x -1 < 7
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Answer
1 ≤ -2x -1 < 7
1+1 ≤ -2x – 1 + 1 < 7+1
2 ≤ -2x < 8
2/(-2) ≤ (-2x)/(-2) < 8/(-2)
-1 ≥ x > -4
Back
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Compound Inequalities for $400
Solve the following inequality:
-5< 7x + 2 ≤ 9
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Answer
-5< 7x + 2 ≤ 9
-5 – 2 < 7x + 2 – 2 ≤ 9 – 2
-7 < 7x ≤ 7
(-7)/7 < (7x)/7 ≤ 7/7
-1 < x ≤ 1
Back
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Compound Inequalities for $500
Write an Inequality to model the following situation:
Mr. Steven is trying to decide whether he wants to buy an automatic or a manual motorbike. If he buys an automatic motorbike, then he will spend at least $850. If he buys a manual bike, then he will spend less than $600.
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Answer
Let C = the cost of the motorbike
Then,
C ≥ $850 or C < $600
Back
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Absolute Value for $100
Define: absolute value
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Answer
Absolute Value – The distance a number is away from zero (the origin)
Back
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Absolute Value for $200
Solve the following inequality:
|3x + 1.5| ≥ 10.5
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Answer
|3x + 1.5| ≥ 10.53x + 1.5 ≥10.5 or 3x + 1.5 ≤ -10.53x ≥ 9 or 3x ≤ -12x ≥ 3 or x ≤ -4
Back
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Absolute Value for $300
Solve the following inequality:
2-3|x+1| = -13
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Answer
2-3|x+1| = -13-3|x+1| = -15|x+1| = 5x+1 = 5 or x+1 = -5x = 4 or x = -6
Back
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Absolute Value for $400
Solve the following inequality:
-5*|x – 3| + 5 > 30
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Answer-5*|x – 3| + 5 > 30
-5*|x – 3| + 5 – 5 > 30 - 5
-5*|x – 3| > 25
(-5*|x – 3|)/(-5) > 25/(-5)
|x – 3| < -5
NO SOLUTION => Absolute Value can never be negative
Back
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Absolute Value for $500
Solve and graph the following inequality:
8 + 2*|3-(2+x)| < 24
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Answer
Back
8 + 2*|3-(2+x)| < 24
8 - 8 + 2*|3-(2+x)| < 24 - 8
2*|3-(2+x)| < 16
|3-(2+x)| < 8
|3-2-x| < 8
|1 – x| < 8
1 - x < 8 and 1 – x > -8
-x < 7 and -x > -9
x > -7 and x < 9