Inequalities - Nicole Forrester
Inequalities Name____________________________
This first worksheet is easy and can be skipped for upper level students.
|1.) Equations have _______________________, but inequalities have |[pic] |
|_______________________________________ | |
| |Fill in the blank with < or > |
|Graph the following: | |
|2.) x < 6 3.) x ( -3 |15.) 2 _____ 3 -2 _____ -3 |
|[pic] [pic] | |
| |1 _____ 4 -1 _____ -4 |
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|4.) 5 > x 5.) 1 ( x |16.) Divide both sides by -1 |
|[pic] [pic] |3 < 5 |
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|6.) x = 7 7.) x ( 2 | |
|[pic] [pic] | |
| |17.) Divide both sides by -2 |
|Write the inequality that goes with the graph: |2 < 4 |
|8.) 9.) | |
|[pic] [pic] | |
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|______________________________________________ |18.) You have to remember to flip the sign when you |
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|“OR” problems have the word __________ in them. |_______________________________by a negative number. |
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|“AND” problems are written in a specific way: |Solve and graph: |
| |19.) [pic] 20.) [pic] |
|L _____ x ______ H | |
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|OR problem AND problem | |
|10.) x < -3 or x ( 5 11.) -4 < x < 7 | |
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|[pic] [pic] | |
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|From the graph, write the inequality | |
|12.) 13.) |21.) [pic] 22.) [pic] |
|[pic] [pic] | |
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|____________________ ____________________ | |
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|Solve and Graph: | |
|14.) x + 5 ( 3 | |
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| |23.) –y < 4 24.) [pic] |
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|25.) Circle all the values of x that COULD be a |31.) 4 + [pic]< 6 |Solve and graph: |
|solution to x < 6 | |36.) -2 ( 3x – 8 ( 10 |
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|x = -10 x = 10 x = -4 x = 4 | | |
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|x = 5 x = -5 x = 200 x = -200 | | |
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|26.) Circle all the values of x that could NOT be a |32.) -3 -6(4x + 6) > -111 | |
|solution to x > -50 | | |
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|x = -10 x = 10 x = -4 x = 4 | | |
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|x = 5 x = -5 x = 200 x = -200 | | |
| | |37.) 3x + 1 < 4 or 2x – 5 > 9 |
|Solve | | |
|27.) 32 ( -16p | | |
| |33.) 5(6 + 3r) + 7 ( 127 | |
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|28.) –⅜x + 4 < 7 | | |
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| | |38.) -2 < -2 – x < 1 |
| |34.) 2x – 4 ( 4x – 1 | |
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|29.) a – 17 > -16 | | |
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| |35.) –x + 1 ( 3x + 21 |39.) 2x + 7 < 3 or 5x + 5 > 10 |
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|30.) -4(2 + n) > -32 | | |
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Inequalities (Word Problems)
|Use [pic], [pic], [pic], [pic] for each of the following. |14.) Write x > 2 and x < 3 in another way |
| | |
|Fewer than | |
| |15.) Write x > 0 and x ≤ 4 in another way |
|More than | |
|At most | |
| |Translate and solve: |
|At least |16.) You make a profit of $1.25 for every book you sell. How many books do |
| |you need to sell to make a minimum of $150? |
|Less than | |
|No less than | |
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|Translate each one into math: | |
| |17.) A student received grades of 92, 95, and 81 on the first three exams. |
|1.) I have LESS THAN 5 dogs. |What grade must the student earn on the fourth exam to get an average of no |
| |less than an A? |
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|2.) I have MORE THAN $3. | |
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|3.) I have between 2 and 8 friends. | |
| |18.) A student received grades of 60, 75, 67, and 62 on the first four |
| |exams. What grade must the student earn on the fifth exam to pass the class? |
|4.) I have at least 4 pens. | |
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|5.) I have at most 6 problems left to do. | |
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| |19.) The length of a rectangle exceeds its width by 8 inches. The perimeter|
|6.) I either have less than 2 cards or more than 8 cards |is at least 80 inches. Find the smallest possible dimensions for the length |
| |and width. |
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|7.) My answer was between 7 and 10. | |
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|8.) An apple has less than 100 calories. | |
| |20.) The width of a rectangle is 4 less than its length. The perimeter is at|
| |most 48 inches. Find the largest possible dimensions for the length and |
|9.) My grade is at least a 70. |width. |
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|10.) The maid has less than 2 rooms to clean. | |
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|11.) The farmer at most 3 tractors. | |
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|12.) She either has less than 5 or more than 9. | |
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|13.) You can have no more than one piece of candy. | |
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Jaden’s Phone Plan (on Mars)
CELL PHONE PLAN A: $20 per month and $.10 per text message
CELL PHONE PLAN B: $10 per month and $.20 per text message
1.) Which plan is better if Jaden only wants to send one text message this month? Explain.
2.) Which plan is better if Jaden wants to send 500 text messages this month? Explain.
3.) What’s the cut off? i.e. When is it better for Jaden to go with one plan over the other plan? Show math.
Best Buy Task
[pic]
1.) Which plan is better if Susie needs to buy tickets for 25 people (i.e. 25 tickets)? Explain.
2.) Which plan is better if Susie needs to buy tickets for 25,000 people (i.e. 25,000 tickets)? Explain.
3.) What’s the cut off? i.e. When is it better for Susie to go with one plan over the other plan? Show math.
Try to find two values that sum to 26. If one value is -69, what is the other number?
What do I have to multiply 7 by to get 210?
A number is taken away from 92 and the result is 9. What is the number?
Two numbers add up to 42. One of the numbers is -13. What is the other number?
A number multiplied by 65 is 3770. What is the number?
The sum of three numbers is 137. The second is 4 more than two times the first. The third is 5 less than three times the first. Find the #’s.
The biology club budgeted $200 for their pancake breakfast. Each meal cost $1.50 to prepare. Write an inequality that represents the number of meals that can be prepared without going over budget.
11.) Write an inequality that represents the statement “I made at least a 70 on my test” and graph the inequality.
12.) Write an inequality that represents the statement “x is less than 5 and is at least -5” and graph the inequality.
The sum of three numbers is 137. The second is 4 more than two times the first. The third is 5 less than three times the first. Find the #’s.
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