Inequality Word Problems 2

Topics

Pre - Algebra

Inequalities

Inequality Word Problems

Inequality Word Problems 2

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 5

Michael wants to buy a new 4K HD TV. The cheapest TV is advertised as

$ 1100

$$1100$ . He has saved

$ 300

$$300$ already and has a part-time job earning

$ 160

$$160$ per week. How many weeks will it take before he has saved up enough to buy the cheapest TV?

1. $n \geq 5$ $n≥5$
2. $n \leq 5$ $n≤5$
3. $n$ $n$ $>$ $>$ $5$ $5$
4. $n$ $n$ $<$ $<$ $5$ $5$

Question 2 of 5

A hard drive holds about

75

$75$ hours of movie videos. So far it has

52

$52$ hours. You estimate that each movie is

2

$2$ hours long. How many movies can we transfer on top of the movies that are already in the hard drive?

1. $n$ $n$ $>$ $>$ $11$ $11$
2. $n$ $n$ $<$ $<$ $11$ $11$
3. $n \geq 11$ $n≥11$
4. $n \leq 11$ $n≤11$

Question 3 of 5

James currently weighs

108

$108$ kg. He wants to weigh less than

90

$90$ kg. If he can lose an average of

1 \frac{1}{2}

$1 1/2$ kg per week through exercise and diet, how long will it take to reach his goal?

1. $n$ $n$ $>$ $>$ $12$ $12$
2. $n$ $n$ $<$ $<$ $12$ $12$
3. $n \geq 12$ $n≥12$
4. $n \leq 12$ $n≤12$

Question 4 of 5

A medium-sized bag of potatoes weighs

1

$1$ kg more than a small bag. A large bag weighs

4

$4$ kg more than a small bag. If the total weight is at most

14

$14$ kg, what is the most that a small bag could weigh?

1. $s$ $s$ $<$ $<$ $3$ $3$
2. $s \geq 3$ $s≥3$
3. $s \leq 3$ $s≤3$
4. $s$ $s$ $>$ $>$ $3$ $3$

Question 5 of 5

5. Question
Jack is flying an air balloon at an altitude of $16000$ feet and is experiencing some bad weather. For him to fly safely, Jack needs to increase his altitude to at least $17000$ feet or decrease his altitude to no more than $13000$ feet. Form an inequality.

The number lines below are scaled as $1:1000$ ft
- 1.
- 2.
- 3.
- 4.
Hint

Help Video
Correct

Exceptional!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

A compound inequality consists of two inequalities joined together by AND or OR.

First, form an inequality from the problem

The height of the balloon must be at least $17000$ feet

$h$ $≥$ $17000$

The height of the balloon must be no more than $13000$ feet

$h$ $≤$ $13000$

$h≥17000$ OR $h≤13000$

The first given inequality has a greater than or equal to ( $≥$ ) sign.

Hence, place a solid circle above $17000$ and attach an arrow pointing to the right to represent all values greater than $17000$ .

The second given inequality has a less than or equal to ( $≤$ ) sign.

Hence, place a solid circle above $13000$ and attach an arrow pointing to the left to represent all values less than $13000$ .

Finally, combine the two number lines.

$300 + 160 n$ $300+160n$	$\geq$ $≥$	$1100$ $1100$
$300 + 160 n$ $300+160n$ $- 300$ $-300$	$\geq$ $≥$	$1100$ $1100$ $- 300$ $-300$	Subtract $300$ $300$ from both sides
$160 n$ $160n$ $\div 160$ $divide160$	$\geq$ $≥$	$800$ $800$ $\div 160$ $divide160$	Divide both sides by $160$ $160$
$n$ $n$	$\geq$ $≥$	$5$ $5$

$52 + 2 n$ $52+2n$	$\leq$ $≤$	$75$ $75$
$52 + 2 n$ $52+2n$ $- 52$ $-52$	$\leq$ $≤$	$75$ $75$ $- 52$ $-52$	Subtract $52$ $52$ from both sides
$2 n$ $2n$ $\div 2$ $divide2$	$\leq$ $≤$	$23$ $23$ $\div 2$ $divide2$	Divide both sides by $2$ $2$
$n$ $n$	$\leq$ $≤$	$11.5$ $11.5$

$108 - 1 \frac{1}{2} n$ $108-1 1/2n$	$<$ $<$	$90$ $90$

$108 - 1 \frac{1}{2} n$ $108-1 1/2n$ $- 108$ $-108$	$<$ $<$	$90$ $90$ $- 108$ $-108$	Subtract $108$ $108$ from both sides

$- 1 \frac{1}{2} n$ $-1 1/2n$ $\div (- 1 \frac{1}{2})$ $divide(-1 1/2)$	$<$ $<$	$- 18$ $-18$ $\div (- 1 \frac{1}{2})$ $divide(-1 1/2)$	Divide both sides by $- 1 \frac{1}{2}$ $-1 1/2$

$n$ $n$	$>$ $>$	$12$ $12$	Flip the inequality

$S$ $S$ $+$ $+$ $M$ $M$ $+$ $+$ $L$ $L$	$\leq$ $≤$	$14$ $14$
$s$ $s$ $+$ $+$ $s + 1$ $s+1$ $+$ $+$ $s + 4$ $s+4$	$\leq$ $≤$	$14$	Substitute the known values
$3s+5$	$≤$	$14$	Combine like terms
$3s+5$ $-5$	$≤$	$14$ $-5$	Subtract $5$ from both sides
$3s$ $divide3$	$≤$	$9$ $divide3$	Divide both sides by $3$
$s$	$≤$	$3$

Inequality Word Problems 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Keep Going!

Identify the known values

2. Question

Hint

Fantastic!

Identify the known values

3. Question

Hint

Well Done!

Identify the known values

4. Question

Hint

Correct!

Identify the known values

5. Question

Hint

Exceptional!

Quizzes

The height of the balloon	must be at least	$17000$ feet
$h$	$≥$	$17000$
The height of the balloon	must be no more than	$13000$ feet
$h$	$≤$	$13000$