Free Practice Quiz Question List

03/14 3. Inequalities Online Quiz Questions

Use this free practice quiz with 20 questions to review 03/14 3. Inequalities, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

True or false: When both sides of an inequality are divided by a negative number, the inequality symbol must be reversed.

A
True
B
False

Choose all

1 point

Select all statements that correctly describe interval notation.

A
$[a,b]$ includes both finite endpoints.
B
$(a,b]$ excludes both finite endpoints.
C
$(a,\infty)$ represents values greater than $a$ , excluding $a$ .
D
$[a,\infty]$ is the standard notation for values at least $a$ .

Written response

1 point

Solve $-3x+5>14$ . Enter the solution inequality.

Fill in the blank

1 point

Solve $-2\le 3x+1<10$ . The solution is $\le x<$ .

Choose one

1 point

For $a>0$ , which description correctly represents the solution set of $|u|>a$ ?

A
The solutions lie between $-a$ and $a$ , including both endpoints.
B
The solutions lie outside $-a$ and $a$ , excluding both boundary points.
C
There are no real solutions.
D
All real numbers are solutions.

True or false

1 point

True or false: The inequality $|x-1|<-2$ has no real solution.

A
True
B
False

Choose all

1 point

Select all correct equivalences for absolute-value inequalities when $a>0$ .

A
$|u|\le a$ is equivalent to $-a\le u\le a$ for $a>0$ .
B
$|u|\ge a$ is equivalent to $u\le -a$ or $u\ge a$ for $a>0$ .
C
$|u|<a$ is equivalent to $u<-a$ or $u>a$ for $a>0$ .
D
$|u|\ge a$ always has solutions only between $-a$ and $a$ for $a>0$ .

Written response

1 point

A student has $\$80$ , pays $\$20$ for admission, and buys notebooks costing $\$6$ each. What is the maximum number of notebooks the student can buy?

Fill in the blank

1 point

When graphing an inequality on a number line, use a for a strict inequality such as $x>3$ , and use a for an inclusive inequality such as $x\ge 3$ .

Choose one

1 point

A delivery center at mile marker 30 serves addresses within 12 miles, including the boundary. If $x$ is the address mile marker, which interval represents the service range?

A
$(18,42)$
B
$[18,42)$
C
$[18,42]$
D
$(18,42]$

Choose one

1 point

Which statement correctly describes how the words “and” and “or” combine solution sets in compound inequalities?

A
“And” means take the union, while “or” means take the intersection.
B
“And” means take the intersection, while “or” means take the union.
C
Both “and” and “or” always mean take the intersection.
D
Both “and” and “or” always mean take the union.

Choose one

1 point

Solve the inequality $4x-7\le 9$ .

A
$x\le 4$
B
$x\ge 4$
C
$x<4$
D
$x>4$

Choose one

1 point

Which number-line description represents $x\ge 3$ ?

A
An open circle at 3 with shading to the left
B
A closed circle at 3 with shading to the right
C
An open circle at 3 with shading to the right
D
A closed circle at 3 with shading to the left

Choose one

1 point

Solve the inequality $-3x+5>14$ .

A
$x>-3$
B
$x\le -3$
C
$x<-3$
D
$x\ge -3$

True or false

1 point

True or false: When both sides of an inequality are multiplied or divided by a negative number, the inequality symbol must be reversed.

A
True
B
False

Written response

1 point

Solve $-2\le 3x+1<10$ and enter the solution in interval notation.

Choose one

1 point

Solve the absolute-value equation $|2x-3|=7$ .

A
$\{-2,5\}$
B
$\{-5,2\}$
C
$\{2,5\}$
D
$\{-2,-5\}$

Choose one

1 point

What is the solution in interval notation for $|x-4|\le 3$ ?

A
$(-\infty,1]\cup[7,\infty)$
B
$[1,7)$
C
$(1,7)$
D
$[1,7]$

Written response

1 point

Solve $|2x+1|>5$ and enter the solution in interval notation.

Open ended

1 point

Solve $7x+4>7x-2$ . State the solution set in inequality notation and interval notation, and explain why the result includes either all real numbers or no real numbers.