Inequalities Study Guide

If  $\frac{3x\ +\ y}{x}$  > 3 and x > 3, which of the following inequalities MUST be true? 

• y > 0

• y > 1

• y > 5

• y > 3

What is the smallest integer for which the inequality is true? $\frac{y}{3}-\ \frac{2}{3}\ \ge\ 2$  

• 8

• 5

• 6

• 7

How many positive integers satisfy the inequality -2 < -5x ?

• None

• One

• Two

• Infinite

Which of the following inequalities has the same solution set as 2x - 3 < -4x - 2 ?

• 2x - 3 > 4x + 2

• -2x + 3 > 4x + 2

• -2x + 3 > 4x - 2

• 2x - 3 > - 4x + 2

Which of the following is a possible value of x if 4x>3and -x>3?

• There are no values

• -5

• -3

• 1

 Which of the following values of x satisfies the inequality  $\frac{2}{5}<x<\frac{4}{5}$  ?

•  $\frac{\sqrt{9}}{5}$  

•  $\frac{\sqrt{16}}{5}$  

•  $\frac{\sqrt{25}}{5}$  

Three times the sum of a number and 9 is at least 48. Let x represent the number. Find all possible values for x.

• $x\ \ge\ 6$

• $x\ \ge\ 7$

• $x\ \ge\ 8$

• $x\ \ge\ 9$

Which of the following values of x satisfies the inequality  $\sqrt{37}<\ x\ <\ \sqrt{65}$  ?

• 6

• 7

• 8

• 9

Mrs. Smith wrote "Nine less than four times a number is greater than twenty" on the board. If x represents the number, which inequality is a correct translation of this statement?

• 4x-9>20

• 4x-9<20

• 9-4x>20

• 9-4x<20

The candy company's total revenue this year was 1.1 times the revenue last year. If they experience the same growth every year, what equation describes how many years will it take before the revenue is more than double?

• $\frac{1.1}{y}$ $\ge$ 2

• $\frac{y}{1.1}$ $\ge$ 2

• 1.1y $\ge$ 2

• 1.1 $y^2$ $\ge$