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Inequalities
Inequalities 2
Compound Ineq
Compound Ineq 2
Ineq Word Problems
100

4x + 2 > 18

x > 4

100

10 - 3x < 28

x > 6

100

10 < 4x + 22 < 14

-3 < x < -2

100

2x + 1 > 3 or 3x < -15

x>1 or x< -5

100
Five less than three times a number is greater than 13. Write the given inequality and solve for the solution.
3x - 5 > 13 x > 6
200

7 - 3x < 10

x > -1

200

18 > 7x + 2x + 9

x > 1

200

2x + 7 > 27 

or 

3 + 3x < 30

x > 10 or x < 9

200

-5x - 8 < -68 or 11x - 12 < -100

x > 12 or x < -8

200
Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a $10 fee. Amanda paid less than $27. Write an inequality to represent the situation. Solve the inequality to find the maximum number of hours Amanda rented the bike.
2x + 10 < 27 x < 8.5 hours
300

2(x + 4) + x < 32

x < 8

300

8x -15 < -16 + 8x

No Solution

300

-36 < 3x - 6 < -15

-10 < x < -3

300

45 < 9 - 12x < 81

-6 < x < -3

300
An online music club has a one-time registration fee of $13.95 and charges $.49 to buy each song. If Emma has $50.00 to join the club and buy songs, what is the maximum number of songs she can buy?
13.95 + .49x < 50 .49x < 36.05, x < 73.6 ------> x < 73 Emma can buy a maximum of 73 songs!
400

-3x - 4(x - 11) > 65

x < -3

400

6 -4(6x + 7) > 122

x < -6

400

5 < 6x - 13 < 17

3 < x < 5

400

x + 18 > 8x + 4 or 15x - 15 < 15x + 5

All real numbers!

400

Jaquan begins his kindergarten year being able to spell 10 words. He is going to learn to spell 2 new words every day. Write an inequality that can be used to determine how many days, d, it takes Jaquan to be able to spell at least 75 words. Use this inequality to determine the minimum number of whole days it will take for him to spell at least 75 words.

10 + 2x > 75

x>37.5 -----> x>38

It will take Jaquan at least 38 whole days!

500

-5 + 2(x - 2) - 5x < -3x + 21

All Real Numbers

500

4(6 + 3x) + 13 > 127 - 3x

x > 6

500

Challenge*

5x + 10 < -4x - 17 < 9 - 2x

-13 < x < -3

500

-47 > 1 - 8x > -63

6 < x < 8

500

Kate has $45 to spend at the fair. She spends $20 on admission and $15 on snacks. She wants to play a game that costs $.65 per game. Write an inequality to find the maximum number of times, x, Kate can play the game. Using this inequality, determine the maximum number of times she can play the game.

45 - 35 > .65x or 10 > .65x 15 > x, 

She can play up to 15 times!