Inequality Word Problems 1

Topics

Precalculus

Inequalities

Inequality Word Problems

Inequality Word Problems 1

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Question 1 of 5

1. Question
The base of a triangle is bigger than its height. Find the possible values of $x$ $x$ .
- 1. $x \leq 4$ $x≤4$
- 2. $x \geq 4$ $x≥4$
- 3. $x$ $x$ $<$ $<$ $4$ $4$
- 4. $x$ $x$ $>$ $>$ $4$ $4$
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Identify the known values

$Base = 11 + x$ $\text(Base)= 11+x$

$Height = 15$ $\text(Height)= 15$

First, form an inequality from the problem

The base of the triangle is bigger than its height

$11 + x$ $11+x$ $>$ $>$ $15$ $15$

Next, make sure that only $x$ $x$ is on the left side

$11 + x$ $11+x$ $>$ $>$ $15$ $15$

$11 + x$ $11+x$ $- 11$ $-11$ $>$ $>$ $15$ $15$ $- 11$ $-11$ Subtract $11$ $11$ from both sides

$x$ $x$ $>$ $>$ $4$ $4$ Evaluate

Check our work

To confirm that $4$ $4$ is less than $x$ $x$ , substitute $x = 5$ $x=5$ to the original inequality

$11 + x$ $11+x$ $>$ $>$ $15$ $15$

$11 +$ $11+$ $5$ $5$ $>$ $>$ $15$ $15$ Substitute $x = 5$ $x=5$

$16$ $16$ $>$ $>$ $15$ $15$

Since the inequality is true, the representation is correct

$x$ $x$ $>$ $>$ $4$ $4$
Question 2 of 5

2. Question
Donald has saved $$ 700$ $$700$ for one-on-one tennis coaching. A coach recommends $20$ $20$ hours of coaching. Write an inequality for the possible hourly rate that Donald could afford to pay for the coaching.
- 1. $r \leq 35$ $r≤35$
- 2. $r$ $r$ $>$ $>$ $35$ $35$
- 3. $r \geq 35$ $r≥35$
- 4. $r$ $r$ $<$ $<$ $35$ $35$
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Identify the known values

$Donald’s savings = $ 700$ $\text(Donald’s savings)= $700$

$Recommended hours of training = 20$ $\text(Recommended hours of training)= 20$

$Rate per hour = r$ $\text(Rate per hour)= r$

First, form an inequality from the problem

Since we know that Donald can only pay a maximum of $$ 700$ $$700$ for $20$ $20$ hours of training, the amount he can pay hourly can only be less than or equal to a certain amount.

Hence, the inequality can be written as:

$\frac{700}{r}$ $700/r$ $\leq$ $≤$ $\frac{20}{1}$ $20/1$

Next, make sure that only $r$ $r$ is on the left side

$\frac{700}{r}$ $700/r$ $\leq$ $≤$ $\frac{20}{1}$ $20/1$

$20 r$ $20r$ $\leq$ $≤$ $700$ $700$ Cross multiply

$20 r$ $20r$ $\div 20$ $divide20$ $\leq$ $≤$ $700$ $700$ $\div 20$ $divide20$ Divide both sides by $20$ $20$

$r$ $r$ $\leq$ $≤$ $35$ $35$

$r \leq 35$ $r≤35$

Question 3 of 5

The perimeter of this triangle must be no more than 75.8 cm. Find an expression that represents all possible

x

$x$ values.

Round your answer to one decimal place

1. $x \leq 25.1$ $x≤25.1$
2. $x \geq 25.1$ $x≥25.1$
3. $x$ $x$ $>$ $>$ $25.1$ $25.1$
4. $x$ $x$ $<$ $<$ $25.1$ $25.1$

Question 4 of 5

The total maximum weight of luggage on a first-class international flight is

50

$50$ kg per person. If Lucy has three suitcases and the first suitcase weighs

17

$17$ kg and the second weighs

15

$15$ kg, how much will the third bag weigh?

1. $x$ $x$ $>$ $>$ $18$ $18$
2. $x$ $x$ $<$ $<$ $18$ $18$
3. $x \geq 18$ $x≥18$
4. $x \leq 18$ $x≤18$

Question 5 of 5

Jane has

$ 85

$$85$ to spend with her friends. They ordered

$ 33

$$33$ worth of pizzas,

$ 11

$$11$ worth of bread and

$ 17

$$17$ on drinks. How much can Jane spend on desserts?

1. $x$ $x$ $>$ $>$ $24$ $24$
2. $x$ $x$ $<$ $<$ $24$ $24$
3. $x \geq 24$ $x≥24$
4. $x \leq 24$ $x≤24$

The perimeter of the triangle	must be no more than	$75.8$ $75.8$
$19.1 + 31.6 + x$ $19.1+31.6+x$	$\leq$ $≤$	$75.8$ $75.8$

$19.1 + 31.6 + x$ $19.1+31.6+x$	$\leq$ $≤$	$75.8$ $75.8$
$50.7$ $50.7$ $+ x$ $+x$	$\leq$ $≤$	$75.8$ $75.8$	Combine like terms
$50.7 + x$ $50.7+x$ $- 50.7$ $-50.7$	$\leq$ $≤$	$75.8$ $75.8$ $- 50.7$ $-50.7$	Subtract $50.7$ $50.7$ from both sides
$x$ $x$	$\leq$ $≤$	$25.1$ $25.1$

$33 + 11 + 17 + x$ $33+11+17+x$	$\leq$ $≤$	$85$ $85$
$61 + x$ $61+x$	$\leq$ $≤$	$85$ $85$	Combine like terms
$61 + x$ $61+x$ $- 61$ $-61$	$\leq$ $≤$	$85$ $85$ $- 61$ $-61$	Subtract $61$ $61$ from both sides
$x$ $x$	$\leq$ $≤$	$24$ $24$

Inequality Word Problems 1

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Quiz summary

Information

1. Question

Hint

Well Done!

Identify the known values

2. Question

Hint

Nice Job!

Identify the known values

3. Question

Hint

Great Work!

4. Question

Hint

Correct!

Identify the known values

5. Question

Hint

Excellent!

Identify the known values

Quizzes

The base of the triangle	is bigger than	its height
$11 + x$ $11+x$	$>$ $>$	$15$ $15$

$\frac{700}{r}$ $700/r$	$\leq$ $≤$	$\frac{20}{1}$ $20/1$
$20 r$ $20r$	$\leq$ $≤$	$700$ $700$	Cross multiply
$20 r$ $20r$ $\div 20$ $divide20$	$\leq$ $≤$	$700$ $700$ $\div 20$ $divide20$	Divide both sides by $20$ $20$
$r$ $r$	$\leq$ $≤$	$35$ $35$

$17 + 15 + x$ $17+15+x$	$\leq$ $≤$	$50$ $50$
$32 + x$ $32+x$	$\leq$ $≤$	$50$ $50$	Combine like terms
$32 + x$ $32+x$ $- 32$ $-32$	$\leq$ $≤$	$50$ $50$ $- 32$ $-32$	Subtract $32$ $32$ from both sides
$x$ $x$	$\leq$ $≤$	$18$ $18$