Linear Inequalities, Course Quiz

Solve

3x + 1 < 13

for natural numbers

x

.

A

\{1, 2, 3, 4\}

B

\{4, 5, 6, \ldots\}

C

\{0, 1, 2, 3\}

D

\{1, 2, 3\}

Solve

2(x - 3) \ge 5x + 6

.

A

x \le -4

B

x \ge -4

C

x \le 4

D

x \ge 4

Solve the system

5x - 2 > 3

and

7 - x \ge 2

.

A

(1, 5)

B

(5, \infty)

C

(1, 5]

D

[1, 5)

Solve

3(x + 2) > 3x + 1

.

A

\displaystyle x > \tfrac{5}{3}

B No real number

C

x > 0

D Every real number

On a number line, a filled (closed) circle at an endpoint means

A the endpoint is included (

\le

or

\ge

)

B the inequality has no solution

C the endpoint is excluded (

<

or

>

)

D the endpoint is

0

Pairs of consecutive even natural numbers are both greater than

5

and add to less than

23

. How many such pairs are there?

A

2

B

5

C

3

D

4

For

4x - y > 3

, the test point

(0, 0)

shows that we shade

A only the line itself

B the side containing the origin

C both sides

D the side not containing the origin

Where does the line

x + 2y = 8

cut the axes?

A

(8, 0)

and

(0, 16)

B

(2, 0)

and

(0, 1)

C

(4, 0)

and

(0, 8)

D

(8, 0)

and

(0, 4)

The region

x + y \le 5

,

x - y \ge -1

,

x \ge 0

,

y \ge 0

has a corner where the two slanting lines meet. Which point is it?

A

(2, 3)

B

(3, 2)

C

(0, 1)

D

(5, 0)

Pens cost ₹

10

and books ₹

40

. Which inequality says that at most ₹

400

is spent on

x

pens and

y

books?

A

10x + 40y \ge 400

B

40x + 10y \le 400

C

10x + 40y \le 400

D

10x + 40y < 400

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