Inequalities

Inequalities

Symbols and Graphs

• When it is only greater or less, that means the boundary point is NOT included in the answer set

• This would be an OPEN circle shaded to the right

Multiple Choice

Which of the solutions matches the graph?

• $x\ge2$
  

• $x>2$

• $x\le2$

• $x<2$

Multiple Choice

Which of the solutions matches the graph?

• $x\le1$

• $x<1$

• $x>1$

• $x\ge1$

But what if it's more than just a variable?

• How would we read 3x > 12?

• What would we do to find possible solutions?

Multiple Choice

Which is a possible solution for $x\ +\ 5\ <\ 7$ 
? 

•  $x>2$  

•  $x<2$  

•  $x>7$  

•  $x<7$  

Multiple Choice

Which is a possible solution for $2x\ \le\ 10$  ?

•  $x\le2$  

•  $x\le10$  

•  $x\le5$  

•  $x\le8$  

But what about more complicated ones with negatives?

When it's not so simple to substitute a value for x, we look for what makes it EQUAL, then we try another number to see if works or not, usually we try 0.

Fill in the Blanks

First solve $2x+4=10$  

Multiple Choice

Now, what if I didn't want exactly 10, but I wanted 2x + 4 to be less than 10. What values would x need to be to make that happen?

• values for x should be more than 3

• values for x should be less than 3

 $-3x+8\ge20$  

•  $-3x+8=20$  

•  $-3x=12$  

•  $x=-4$  

• Now, since we know that when x = -4 we get exactly 20, we need to find values for x that would give us MORE THAN 20

• Does using 0 for x give us more than 20?

•  $-3\left(0\right)+8\ge20$  

•  $8\ge20$  FALSE

 $-3x+8\ge20$  

• Since we know x= -4 and 0 is NOT a possible solution...

• What would our number line look like?

Multiple Select

 $4x-8\ge12$  

If this is our original problem, what answer choices could you ELIMINATE right away by looking at the inequality symbol?