Framing and Solving Inequalities

Solving Inequalities

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Inequalities are just like equations, but without the = sign.

What do the symbols mean?

Solving Inequalities

• Use the same steps that you would use to solve an equation.

• But remember the Golden Rule: If you multiply or divide by a NEGATIVE when you are solving an inequality, then you must FLIP the inequality symbol.

• If the variable does not end up on the left when you solve, then rewrite the inequality (backwards) before you're done. For example, 4>x would be rewritten as x<4.

Multiple Choice

$$Solve:\ 5\left(2+2x\right)>90$$  

• $$x<8$$  

• $$x<-36$$  

• $$x>8$$  

• $$x>-31$$  

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Multiple Choice

$$Solve:\ -7\left(n-6\right)<91$$  

• $$n<7$$  

• $$n>7$$  

• $$n<-7$$  

• $$n>-7$$  

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Multiple Choice

$$Solve:\ -82>2\left(n-5\right)+7n$$  

• $$n>-25$$  

• $$n<-25$$  

• $$n<-8$$  

• $$n>-8$$  

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Graphing the Solution to an Inequality

Multiple Choice

Which one shows the graph of the solution?

$$x\le5$$  

Draw

Solve and graph the inequality.

Draw

Solve and graph the inequality

Poll

How do we feel about inequalities?