Inequalities



Inequalities Name____________________________

|1.) Equations have _______________________, but |Fill in the blank with < or > |

|inequalities have | |

|_______________________________________ |14) 2 _____ 3 -2 _____ -3 |

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|Graph the following: |1 _____ 4 -1 _____ -4 |

|2.) x < 6 3.) x ( -3 | |

|[pic] [pic] |15) Divide both sides by -1 |

| |3 < 5 |

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|4.) 5 > x 5.) 1 ( x | |

|[pic] [pic] | |

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| |16) Divide both sides by -2 |

|6.) x = 7 7.) x ( 2 |2 < 4 |

|[pic] [pic] | |

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|Write the inequality that goes with the graph: | |

|8.) 9.) |17) You have to remember to flip the sign when you |

|[pic] [pic] | |

| |_______________________________by a negative number. |

|______________________________________________ | |

| |Solve and graph: |

|“OR” problems have the word __________ in them. |18) [pic] 19) [pic] |

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|“AND” problems are written in a specific way: | |

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|L _____ x ______ H | |

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|OR problem AND problem | |

|10.) x < -3 or x ( 5 11.) -4 < x < 7 | |

| |20) [pic] 21) [pic] |

|[pic] [pic] | |

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|From the graph, write the inequality | |

|12.) 13.) | |

|[pic] [pic] | |

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|____________________ ____________________ |22) –y < 4 23) [pic] |

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|25.) Circle all the values of x that COULD be a | 31) -3 -6(4x + 6) > -111 |36) 3x + 1 < 4 or 2x – 5 > 9 |

|solution to x < 6 | | |

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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 | | |

|solution to x > -50 | | |

| |32) 5(6 + 3r) + 7 ( 127 | |

|x = -10 x = 10 x = -4 x = 4 | |37) -2 < -2 – x < 1 |

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|x = 5 x = -5 x = 200 x = -200 | | |

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|Solve | | |

|27.) 32 ( -16p | | |

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| |33) 2x – 4 ( 4x – 1 | |

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| | |38) 2x + 7 < 3 or 5x + 5 > 10 |

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|28.) –⅜x + 4 < 7 | | |

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| |34) –x + 1 ( 3x + 21 | |

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| | |39) Write x > 0 and x ≤ 4 in another way |

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|29) -4(2 + n) > -32 | | |

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| |Solve and graph: | |

| |35) -2 ( 3x – 8 ( 10 | |

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|30) 4 + [pic]< 6 | | |

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Inequalities (Word Problems)

|Use [pic], [pic], [pic], [pic] for each of the following. |Translate and solve: |

| |14.) You make a profit of $1.25 for every book you sell. How many books do |

|Fewer than |you need to sell to make a minimum of $150? |

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|More than | |

|At most | |

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|At least | |

| |15.) A student received grades of 92, 95, and 81 on the first three exams. |

|Less than |What grade must the student earn on the fourth exam to get an average of no |

|No less than |less than an A? |

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|Translate each one into math: | |

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|1.) I have LESS THAN 5 dogs. | |

| |16.) 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? |

|2.) I have MORE THAN $3. | |

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|3.) I have between 2 and 8 friends. | |

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| |17.) The length of a rectangle exceeds its width by 8 inches. The perimeter|

|4.) I have at least 4 pens. |is at least 80 inches. Find the smallest possible dimensions for the length |

| |and width. |

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|5.) I have at most 6 problems left to do. | |

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|6.) I either have less than 2 cards or more than 8 cards | |

| |18.) 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 |

|7.) My answer was between 7 and 10. |width. |

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|8.) An apple has less than 100 calories. | |

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|9.) My grade is at least a 70. | |

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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.) 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.

A) Write an inequality that represents the statement “I made at least a 70 on my test” and graph the inequality.

B) Write an inequality that represents the statement “x is less than 5 and is at least -5” and graph the inequality.

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