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$300 $300 $300 $300

$400 $400 $400 $400

$500 $500$500 $500

Graphing Inequalities

One Step Inequalities

Absolute Value

Multi-Step Inequalities

Compound Inequalities

Graphing Inequalities for $100

Graph the inequality shown below:

x > -4

Answer

Back

X > -4

Graphing Inequalities for $200

Write an inequality for the graph shown below:

Answer

Back

X ≤ 3

Graphing Inequalities for $300

Graph the inequality shown below:

-7 < x

Answer

Back

-7 < x

Graphing Inequalities for $400

Graph the inequality shown below:

0 ≤ x < 4

Answer

Back

0 ≤ x < 4

Graphing Inequalities for $500

Graph the inequality shown below. Check your answer:

x < -5 or x ≥ 2

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

One-Step Inequalities for $100

Solve for x:

X + 2 < 1

Answer

X + 2 < 1 -2 -2X < -1

Back

One-Step Inequalities for $200

Solve for x:

x/(-5) > 7

Answer

x/(-5) > 7

x/(-5) * (-5) > 7 * (-5)

X < -35

Back

One-Step Inequalities for $300

Solve for x:

4x ≥ -36

Answer

4x ≥ -36

(4x)/(4) ≥ (-36)/(4)

x ≥ -9

Back

One-Step Inequalities for $400

Write the following inequality in words:

x + 5 ≥ 7

Answer

Back

x + 5 ≥ 7

Five more than a number, x, is greater than or equal to 7

One-Step Inequalities for $500

Write an Inequality to model the following situation:

Mr. Sam spent at least 4 hours making this game

Answer

Back

Let t = the time Mr. Sam spent making this game

Then,

t ≥ 4 hours

Multi-Step Inequalities for $100

Solve for x:

x/(3) + 3 > 5

Answer

x/(3) + 3 > 5x/(3) + 3 - 3 > 5 - 3x/(3) > 2x/(3) * 3 > 2 * 3X > 6

Back

Multi-Step Inequalities for $200

Solve for x:

-5x + 20 ≤ 10

Answer

-5x + 20 ≤ 10 -20 -20-5x ≤ -10(-5x)/(-5)≤ (-10)/(-5)X ≥ 2

Back

Multi-Step Inequalities for $300

Replace the with a number that makes the inequalities equivalent

-3x >

x < -9

Answer

-3x > (-3x)/(-3) > / (-3)x < /(-3) and x < -9So, /(-3) = -9 /(-3) * -3 = -9 * -3 = 27

Back

Multi-Step Inequalities for $400

Solve for x:

-(x-6) + 5 - 2x < 8

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

Multi-Step Inequalities for $500

Solve for x. CHECK YOUR ANSWER

10x – 5 - 3x > 3 – (5 - x)

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

Compound Inequalities for $100

Write a compound inequality that models the graph:

Answer

X < -3 or X ≥ -1

Back

Compound Inequalities for $200

Solve the following inequality:

|-2(3-x) +2| -1 > 11

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

Compound Inequalities for $300

Solve the following inequality:

1 ≤ -2x -1 < 7

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

Compound Inequalities for $400

Solve the following inequality:

-5< 7x + 2 ≤ 9

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

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.

Answer

Let C = the cost of the motorbike

Then,

C ≥ $850 or C < $600

Back

Absolute Value for $100

Define: absolute value

Answer

Absolute Value – The distance a number is away from zero (the origin)

Back

Absolute Value for $200

Solve the following inequality:

|3x + 1.5| ≥ 10.5

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

Absolute Value for $300

Solve the following inequality:

2-3|x+1| = -13

Answer

2-3|x+1| = -13-3|x+1| = -15|x+1| = 5x+1 = 5 or x+1 = -5x = 4 or x = -6

Back

Absolute Value for $400

Solve the following inequality:

-5*|x – 3| + 5 > 30

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

Absolute Value for $500

Solve and graph the following inequality:

8 + 2*|3-(2+x)| < 24

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