Two Step Inequalities

Two Step Inequalities

by Scott Donnelly

​Steps to Solve 2 Step Inequality

​The steps to solve an inequality. Steps might be skipped, if needed

1. Use addition or subtraction to get the variable alone.

2. Use multiplication or division to get the variable alone

   1. If you multiply or divide by a negative number, you must flip the inequality sign.

3. Graph the line

   1. Determine if open or closed dot.

   2. Graph the line, make sure to put an arrow at the end.

Multiple Choice

What would be the first step to solve this equation?

$$2x+4=-12$$  

• Add 4 to both sides.

• Divide by 2 to both sides.

• Multiply by 2 to both sides.

• Subtract 4 from both sides

Multiple Choice

Solve the equation

$$2x+4=-12$$  

• $$x=-4$$  

• $$x=-8$$  

• $$x=8$$  

• $$x=4$$  

​Example

​The steps to solve the inequality and equality are the same.

​The only difference is graphing the inequality.

Multiple Choice

What is first step to solve this inequality

$$3x-4<-19$$  

• Add 4 to both sides

• Divide by 3 to both sides

• Subtract 4 from both sides.

• Multiply 3 to all terms.

Multiple Choice

After first step, what will inequality look like?

$$3x-4<-19$$  

• $$3x>-15$$  

• $$3x<-15$$  

• $$3x<-19$$  

• $$3x>-15$$  

Multiple Choice

What will you divide by and will you flip the inequality sign

$$3x<-15$$  

• 3 and yes

• -3 and yes

• 3 and no

• -3 and no

Multiple Choice

What is the final answer

$$3x<-15$$  

• $$x<-5$$  

• $$x>-5$$  

• $$x>5$$  

• $$x<5$$  

Multiple Choice

What will the graph look like?

$$x<-5$$  

• Closed and to the right

• Closed and to the left

• Open and to the right

• Open and to the left

Multiple Choice

Will you flip the inequality symbol?

$$-5x+4<29$$  

• Yes

• No

Multiple Choice

Solve the inequality, what is your answer?

$$-5x+4<29$$  

• $$x>-5$$  

• $$x<-5$$  

• $$x>-7$$  

• $$x>5$$  

Multiple Choice

What is the first step

$$\frac{x}{2}+4<-8$$  

• Add 4 to both sides

• Multiply 2 to both sides

• Subtract 4 from both sides

• Divide everything by 2

Multiple Choice

After first step you are left with, what is next step

$$\frac{x}{2}<-12$$  

• Multiply 2 to both sides

• Divide by 2

• Divide everything by 2

Multiple Choice

Will you flip the sign

$$\frac{x}{2}<-12$$  

• Yes

• No

Multiple Choice

What is the final answer

$$\frac{x}{2}<-12$$  

• $$x<-6$$  

• $$x>-6$$  

• $$x<-24$$  

• $$x>-24$$