# SOLVING INEQUALITIES PRACTICE WORKSHEET FOR SAT

Problem 1 :

An online office supply store sells pens at p dollars per box and offers free shipping on orders of \$75 or more. If John decides to order new pens from this store, which of the following inequalities expresses the number of boxes n that he must purchase for the order to qualify for free shipping ?

a)  n ≤ (p/75)        b)  n  ≥ p/75    c) n ≤ 75/p    d)  n ≥ 75/p

Solution

Problem 2 :

≤ 3x + 1

x - y > 1

Which of the following ordered pairs (x, y) satisfies the system of inequalities above ?

a)  (-2, -1)    b) (-1, 3)    c) (1, 5)    d)  (2, -1)

Solution

Problem 3 :

Which of the following numbers is NOT a solution of the inequality 3x − 5 ≥ 4x −3 ?

a) −1     b) −2     c) −3      d) −5

Solution

Problem 4 :

y < -x + a, y > x + b

In the xy plane if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true ?

a)  a > b    b) b > a     c) |a| > |b|      d) a = -b

Solution

Problem 5 :

≤ -15x + 3000

y ≤ 5x

In the xy plane, if the point with coordinates (a, b) lies in the solution to the set of inequalities above, what is the maximum possible value of b ?

Solution

Problem 6 :

The total cost, in dollars, to rent a surfboard consists of a \$25 service fee and a \$10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximum of \$75 to rent the surfboard. Which inequality represents this situation?

A) 10t ≤ 75     B) 10 + 25t ≤ 75    C) 25t ≤ 75

D) 25 + 10t ≤ 75

Solution

Problem 7 :

A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?

A) p > 0.20 (300−36),where p ≤ 150

B) p > 0.20 (300+36), where p ≤ 150

C) p - 36 > 0.20 (300), where p ≤ 150

D) p + 36 > 0.20 (300), where p ≤ 150

Solution

1)  n ≥ 75/p

2) x = 2 and y = -1, option d is correct.

3)  So, option a is not a solution.

4)  a > b, option a is correct.

5)  the maximum value of b is 750.

6)  25 + 10t ≤ 75

7)  (p+36) ≥ 0.20(300), where p ≤ 150

So, option d is correct

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