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.

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?