Lesson: Solving Multi-Step Equations and Inequalities

Lesson 8-6: Solving Multi-Step Equations and Inequalities

p. 374

 $12m+12=6\left(3m+3\right)$  

• What is the first step to solving this equation?

• Let’s work this out together.

• Be sure to check your solution!

No Solution

• Some equations have no solution.

• When this happens, the solution is the null or empty set.

• We use the symbols  $\theta\ or\ \left\{\ \right\}$ .

Multiple Select

Solve the equation. Check your solution. 

Select 2 answers.

 $-2\left(3r+4\right)=-5r-8-r$  

• Identity

• Null, or empty, set

• All numbers

• No solution

All Numbers

• Other equations may have every number as their solution.

• An equation that is true for every value of the variable is called an identity.

• An identity is an equation that shows that a number of expression is equivalent to itself.

• Additive Identify:  $a+0=a$  

• Multiplicative Identity:  $a\cdot1=a$  

Multiple Select

Solve the equation. Check your solution. 

Select 2 answers.

 $14+8w=4\left(8+2w\right)$  

• Identity

• Null, or empty, set

• All numbers

• No solution

Multiple Select

 $7y-8=3\left(2y+4\right)+y$  

• Identity

• Null, or empty, set

• All numers

• No solution

Multiple Select

 $3\left(4x-2\right)+15=12x+9$  

• Identity

• Null, or empty, set

• All numers

• No solution

Inequalities!

Multiple Choice

Solve. Check your solution.

 $3<4\left(x+2\right)$  

•  $x>-1.25$  

•  $x<-1.25$  

•  $x>1.25$  

•  $x<1.25$  

Multiple Choice

Solve. Check your solution.

 $4\left(b-3\right)\le72$  

•  $b\ge21$  

•  $b\le60$  

•  $b\le21$  

•  $b\le15$  

Partners:

p. 377 #1-17 ODD

Independent:

p. 377 #18-36 EVEN