SOLVING LINEAR INEQUALITIES IN ONE VARIABLE REVIEW WORKSHEET

Problem 1 :

What are the solutions to the following inequality ?

4x ≥ 68

A. x > 64 B. x ≥ 64 C. x > 17 D. x ≥ 17

Solution

Problem 2 :

What are the solutions to the following inequality ?

2x + 6 < 4

A. x < 1    B. x < -1     C. x > 1    D. x > -1

Solution

Problem 3 :

Melissa has $20 to buy bagels and juice for her class.

Box of bagels  $6.13, including tax

Bottle of juice $2.08, including tax

She will buy one box of bagels, with the rest of the money, Melissa will buy as many bottles of juice as possible. Which inequality can she use to find b, the maximum number of bottles of juice she can buy ?

A. 6.13b + 2.08 ≤ 20.00    B. 6.13 + 2.08b ≤ 20.00 

C.6.13b + 2.08 ≥ 20.00     D. 6.13 + 2.08b ≥ 20.00

Solution

Problem 4 :

The picture of the balance shown below models an inequality.

What solutions make the inequality true ?

A.x > 3    B x < 3     C x > 6     D x < 6

Solution

Problem 5 :

Which inequality best represents the solution set shown on the number line?

A. n < -1     B. n ≤ -1     C. n > -1    D. n ≥ -1

Solution

Problem 6 :

Which graph best represents the solution set for the following inequality ?

5n + 2 ≤ 12

Solution

Problem 7 :

When x is an integer, what is the solution set of 5 ≤ x < 8 ?

A. [5, 6, 7, 8]      B. [5, 6, 7] 

C. [6, 7, 8]     D [6, 7]

Solution

Problem 8 :

The inequality 3x + 2 > x + 8 is equivalent to

A. x > -1/2     B. x  > 3/2    C. x > 3    D. x < 3

Solution

Problem 9 :

Chris runs a barber’s shop. It costs him 20 per day to cover his expenses and he charges 4 for every hair cut

(a) Explain why his profit for any day is (4x – 20), where x is the number of haircuts in that day.

He hopes to make at least 50 profit per day, but does not intend to make more than 120 profit.

(b) Write down an inequality to describes this situation.

(c) Solve the inequality.

Solution

Problem 10 :

The distance that a car can travel on a full tank of petrol varies between 200 and 320 miles.

(a) If m represents the distance (in miles) travelled on a full tank of petrol, write down an inequality involving m

(b) Distance in kilometers, k, are related to distances in miles by

m = 5k/8.

Write down an alternative inequality involving k instead of m.

(c) How many kilometers can the car travel on a full tank of petrol ? 

Solution