Algebra 1 - Inequalities Review

Everyone in your family is older than 3 but younger than 97. Express this fact using interval notation.

(3, 97)

Solve the following inequality: |x + 6| ≤ 4

-10 ≤ x ≤ -2

Fill in the blank -3 _____ -√11

>

Fill in the blank 2 + √5 _____ 7 - √10

>

Which type of compound inequality has these two features? 1. In order for the solution to work, both conditions must be true. 2. It has a less than symbol.

And

Which symbol is this? ≤

Less than or equal to

Typically, an inequality can have how many solutions?

Multiple solutions

When the arrows of an inequality go in opposite directions, or the absolute value is greater than, what type of a compound inequality are we working with?

Or

What part of this graph is the solution area for a system of inequalities? study.com/cimages/multimages/16/graphing_inequalities_q5.jpg

The overlapping part

Which rule do you need to remember when solving a 1-variable absolute value inequality?

When undoing an absolute value, you must flip the inequality symbol on the negative solution.

Which of the answer choices is an INCORRECT statement? a. -2 < -4 b. 24 < 25 c. 0 > -1 d. 2/3 > 0.15

a. -2 < -4

Which of the following is an example of an inequality? a. 60 + 2x < 120 b. 60 + |-3| = 63 c. 60 - 2(15) = 130 d. 60 + 2x = 120

a. 60 + 2x < 120

Which sentence best describes the 'AND' compound inequality? a. A problem with two 1-variable inequalities where the conditions in both must be satisfied in order to be a solution b. A problem with two 2-variable inequalities where only one condition in each must be satisfied in order to be a solution c. A problem with two 2-variable inequalities where both conditions in each must be satisfied in order to be a solution d. A problem with two 1-variable inequalities where only one condition in each must be satisfied in order to be a solution

a. A problem with two 1-variable inequalities where the conditions in both must be satisfied in order to be a solution

A mathematician goes shopping and sets his budget (in dollars) using the following set notation {x | x > 50 and x < 75} where x is the amount he will spend. Which of the following is within his budget? a. $50 b. $53 c. $49 d. $75

b. $53

Which set of numbers make this inequality true? a < b a. a = 0 b = -0.1 b. a = √9 b = 3 c. a = pi b = 3.5 d. a = √8 b = √7 e. a = -3 b = -7

c. a = pi b = 3.5

This equation is an example of which one of the following? Ax + By > C a. An inequality with only one solution b. A one-variable inequality c. A two-variable inequality d. A three-variable inequality

c. A two-variable inequality

Which statement is INCORRECT about inequalities? a. One of the inequality symbols is < b. They can be used with all real numbers. c. One of the inequality symbols is = d. They represent the relationship between two numbers.

c. One of the inequality symbols is =

Which statement would be represented by an inequality? a. The concert tickets cost $75 per ticket. b. The turkey needs to cook for exactly four hours. c. To ride the roller coaster you must be at least four feet tall. d. The fence is 12 feet long.

c. To ride the roller coaster you must be at least four feet tall.

Which sentence best describes an 'OR' compound inequality? a. A problem with two 2-variable inequalities where only one condition must be satisfied in order to be a solution b. A problem with two 1-variable inequalities where both conditions must be satisfied in order to be a solution c. A problem with two 2-variable inequalities where both conditions must be satisfied in order to be a solution d. A problem with two 1-variable inequalities where only one condition must be satisfied in order to be a solution 3. Which sentence best describes the 'A

d. A problem with two 1-variable inequalities where only one condition must be satisfied in order to be a solution

Which of the following is a type of inequality sign? a. > b. < c. ≥ and ≤ d. All of the answers are correct.

d. All of the answers are correct.

Which of the following is the greater than or equal to symbol? a. > b. < c. = d. ≥ e. ≤

d. ≥

Which of the following is the math sentence of the following inequality? x - 7 ≤ 2 a. A number plus 7 is less than 2. b. A number minus 7 is less than 2. c. A number is less than 9. d. A number plus 7 is greater than 2. e. A number minus 7 is less than or equal to 2.

e. A number minus 7 is less than or equal to 2.

Graph the following inequality: |x| > 2

study.com/cimages/multimages/16/1348995265_op3.png

Write the inequality for: A number minus 10 is less than 20.

x - 10 < 20

Solve the following inequality: 2x + 4 < 20.

x < 8

Solve the following inequality: x + 2 > 10.

x > 8

Write the inequality for: A number is greater than 95.

x > 95

This graph corresponds to which inequality? study.com/cimages/multimages/16/graphing_inequalities_q1.jpg

y > 4x - 3

This graph corresponds to which inequality? study.com/cimages/multimages/16/graphing_inequalities_q2.jpg

y ≥ x + 4

The solution set is all values of x, such that x is greater than 30, and less than 45. Express the solution set for this compound inequality using set notation.

{x | x > 30 and x < 45}