Inequalities

Inequalities

Understand solving an inequality as a process of answering a question: which values from a specified set, if any, inequality true? Use substitution to determine whether a given number in a specified set makes the inequality true.

Inequality

The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than, .” $\le$ "less than or equal to,  $\ge$  "greater than or equal to". 

Multiple Choice

What is this symbol?

• less than

• greater than

• less than or equal to

• greater than or equal to

Examples of Inequalities

• x + 3  $\ge$ 10

• y+1 $\le$  5

• x  $>$  5

• y $<$  6

Multiple Choice

What symbol could go in the box to make a true statement?
9 ___  -9

• >
• <
• ≥
• ≤

Multiple Choice

Which of these means that x is greater than or equal to 12

• x ≥ 12
• x  > 12
• x ≠ 12
• x ≥ 15

Steps to determine if a number is part of the solution set:

1. Read the inequality from the variable and put it in your own words

2. substitute the given number and evaluate

3. Decide if the number makes the inequality true.

Multiple Select

Which set (s) of numbers make the inequality a - 5 < 6

• { 8,9,10}

• {11,12,13}

• {5,6,7}

Multiple Choice

No More Than

• <
• >
• ≤
• ≥

Multiple Choice

Fewer Than

• <
• >
• ≤
• ≥

Multiple Choice

more than

• <
• >
• ≤
• ≥

Graphing Inequalities

In the inequality x > 6, the number 6 is not part of the solution set. Here is why...

6 > 6 ---- Six is not greater than six !

Therefore, when graphing, I will start from 6 but not include six as part of my solution set. 
x  $\ge$  6  ------- In this inequality six is part of the solution. Here is why....

6  $\ge$  6  ---------   6 makes the inequality  true because of  "or equal than"