1.5 - Solve Linear Inequalities

1.5 - Solve Linear Inequalities

If you can solve equations, you already know 95% of what you need to know to solve inequalities.

The properties of equality are true for inequalities, with one main difference

• If you multiply both sides of the inequality by the same negative number, you must reverse the inequality symbol

• If you divide both sides of the inequality by the same negative number, you must reverse the inequality symbol

Example:

 $9x+4<12x-11$  
 $-12x\ \ \ \ \ \ \ -12x$  
 $-3x+4<-11$  
 $\ \ \ \ \ \ \ \ \ -4\ \ \ \ \ \ -4$  
 $-3x<-15$  
 $\frac{-3x}{-3}\ \ >\frac{-15}{-3}$  
 $\ \ \ \ \ x\ >5\$  

Multiple Choice

Solve

 $x+8\ge4x+17$  

•  $-3\ge x$  

•  $-3\le x$  

•  $3\ge x$  

•  $3\le x$  

Multiple Choice

The solution to which inequality is represented by this graph?

• $5x+3<3x+9$

• $\frac{x}{4}\ge12$

• $5x+3>3x+9$

• $3x<-9$

Open Ended

Solve the inequality:

 $-3x+8\le14$  

Open Ended

Write a two-step inequality that has a solution of

 $x<4$