Properties of Inequalities

Properties of Inequalities

Multiple Choice

 $3<10$  

• True

• False

Multiple Choice

 $3+2<10+2$  

• True

• False

Multiple Choice

 $3-2<10-2$  

• True

• False

Multiple Choice

Analyzing the last three questions do you believe the property of inequality for +/- will always hold true similar to the property of equality

• Yes

• No

You can add to or subtract from both sides of an inequality to solve for x

Multiple Choice

 $3\left(2\right)<10\left(2\right)$  

• True

• False

Multiple Choice

 $3\left(-2\right)<10\left(-2\right)$  

• True

• False

Property of Multiplication/Division

• when multiplying by a positive number:
   $3\left(2\right)<10\left(2\right)$            $6<20$  
  

• When multiplying by a negative number (the sign flips):

   $3\left(-2\right)\ is\ not\ <\ 10\left(-2\right)\ \ \ \ \ \ \ \ \ \ \ \ \ -6>-20$  

Multiple Choice

 $\frac{3}{2}<\frac{10}{2}$  

• True

• False

Multiple Choice

 $\frac{3}{-2}<\frac{10}{-2}$  (Be Careful! Is - 1.5 less than or greater than - 5)

• True

• False

Open Ended

Analyzing the last four questions What do you notice about the property of inequality for x / $\div$ 

Multiple Choice

Does the property of equality hold true for x/ $\div$  by a positive number ?

• Yes

• No

Multiple Choice

Does the property of equality hold true for x/ $\div$ by a negative number ?

• Yes

• No

Lesson Video

Properties of Inequalities

Multiple Choice

Given that  $-2x\ >-1\ \ \$ 
Which statment is True? (Hint: Use the properties for solving for x)

•  $x\ <\ \frac{1}{2}$ 

•  $x>\frac{1}{2}$ 

•  $x>-\frac{1}{2}$  

•  $x>1$  

Multiple Choice

Given that  $-2x\ >1\ \ \$ 
Which statment is True?

•  $x\ <\ -\frac{1}{2}$ 

•  $x>-\frac{1}{2}$ 

Multiple Choice

Given that  $2x\ >-\ 1\ \ \$ 
Which statment is True?

•  $x\ <\ \frac{-1}{2}$ 

•  $x>\frac{-1}{2}$ 

Multiple Choice

Given that  $2x\ >\ 1\ \ \$ 
Which statment is True?

•  $x\ <\ \frac{1}{2}$ 

•  $x>\frac{1}{2}$ 

Multiple Choice

Given that $x\ \le\ y\ \ \$
Which statment is True? (Hint: check the signs carefully)

• $\frac{x}{-2}\ \le\ \frac{y}{-2}$

• $\frac{x}{-2}\ge\frac{y}{-2}$

Multiple Choice

Given that $x\ \le\ y\ \ \$
Which statment is True?

• $\frac{x}{2}\ \le\ \frac{y}{2}$

• $\frac{x}{2}\ge\frac{y}{2}$

Multiple Choice

Given that $x\ \le\ y\ \ \$
Which statment is True?

• $-2x\ \le\ -2y$

• $-2x\ \ge-2y$

Multiple Choice

Given that  $x\ \le\ y\ \ \$  
Which statment is True? 

•  $2x\ \le\ 2y$  

•  $2x\ \ge2y$  

Multiple Select

Given that  $x\ >\ 2\ is\ True.$  
Which statments are True? 

•  $2x\ >\ 4$  

•  $-2x\ >\ 4$  

•  $-2x\ <\ -4$  

•  $-5x\ >\ -10$