2-Step Equations

Two-Step Equations

When solving two-step equations...

Use the inverse operations in REVERSE order of the order of operations

Multiple Choice

In the equation below, what is the forward order of operations?

 $3x+2=23$  

• Multiply by 3, then add 2.

• Add 2, then multiply by 3.

Multiple Choice

If the correct forward order is to multiply by 3 and then subtract 2, what is the first inverse operation we need to perform to solve this? $3x+2=23$  

• Divide by 3.

• Subtract 2.

 $3x+2=23$  

 $3x+2=23$  
       $-2\ \ \ \ \ -2$    Subtract 2 from both sides.

   $3x=21$        

Multiple Choice

What is the second inverse operation that needs to be performed on the resulting equation $3x=21$ ?

• Multiply by 3.

• Divide by 3.

• Add 3.

• Subtract 3.

 $3x+2=23$  

 $3x+2=23$  
       $-2\ \ \ \ \ -2$     Subtract 2 from both sides.

   $3x=21$        

  $\frac{3x}{3}\ \ \ \ \frac{21}{3}$     Divide both sides by 3.

 $x=7$  

Check your work

 $3x+2=23$  Plug in 7 got x.

 $3\left(7\right)+2=?$  

 $21+2\ =\ 23$  Correct!

Multiple Choice

In the equation $4+\frac{1}{5}r=-1$ , what is the first inverse operation that should be performed to solve it?

• Subtract 4 from both sides.

• Multiply both sides by 5.

 $4+\frac{1}{5}r=-1$  

 $4+\frac{1}{5}r=-1$ 
 $-4\ \ \ \ \ \ \ \ \ \ \ -4$    Subtract 4 from both sides.

       $\frac{1}{5}r=-5$   

Multiple Select

What is the next inverse operation that should be used to solve this? Select all that apply.
 $\frac{1}{5}r=-5$  

• Divide both sides by 5.

• Multiply both sides by 5.

• Divide both sides by 1/5.

• Multiply both sides by 1/5.

 $4+\frac{1}{5}r=-1$  

 $4+\frac{1}{5}r=-1$ 
 $-4\ \ \ \ \ \ \ \ \ \ \ -4$      Subtract 4 from both sides.
       $\frac{1}{5}r=-5$   

 $\left(5\right)\frac{1}{5}r=-5\left(5\right)$   Multiply both sides by 5 (or divide by 1/5).

 $r=-25$  

Check your work

 $4+\frac{1}{5}r=-1$  Plug in -25 for r.

 $4+\frac{1}{5}\left(-25\right)=?$  

 $4+\left(-5\right)=-1$  Correct!

Multiple Choice

In the equation below, what is the correct forward order of operations? $5\left(n-2\right)=-30$  

• Multiply by 5, then subtract 2.

• Subtract 2, then multiply by 5.

Open Ended

 $5\left(n-2\right)=-30$  

Why does subtraction come before multiplication in this equation?

 $5\left(n-2\right)=-30$  

The forward order of operations is subtraction, then multiplication.

So in order to solve this, we have to undo the multiplication first. 

We DIVIDE BOTH SIDES BY 5. 

 $\frac{5\left(n-2\right)}{5}=\frac{-30}{5}$  

This leaves us with  $n-2=-6$  

Imagine it this way....

 $5\left(x-2\right)=-30$  

Five groups of (x-2) equal -30.
So when we divide both sides by 5, we can see that one group of (x-2) equals -6.

Multiple Choice

 $3(x+5)=18$  
In this equation, what is the first inverse operation that should be performed in order to solve this?

• Subtract 5 from both sides.

• Divide both sides by 3.

 $3\left(x+5\right)=18$  

 $3\left(x+5\right)=18$  

 $\frac{3\left(x+5\right)}{3}\ \ \ \frac{18}{3}$     Divide both sides by 3.

 $x+5=6$  

 

Multiple Choice

What is the next inverse operation that needs to be performed in order to solve the equation?

 $x+5=6$  

• Subtract 5 from both sides.

• Add 5 to both sides.

 $3\left(x+5\right)=18$  

 $3\left(x+5\right)=18$  

 $\frac{3\left(x+5\right)}{3}\ \ \ \frac{18}{3}$     Divide both sides by 3.

 $x+5=6$  

    $-5\ \ \ \ -5$         Subtract 5 from both sides.

 $x=1$   

Check your work

 $3\left(x+5\right)=18$  

Plug 1 in for x.
 $3\left(1+5\right)=?$  

 $3\left(6\right)=18$  Correct!

Multiple Choice

 $\frac{2}{3}\left(x-13\right)=22$  
What is the first step we would take to solve this equation? (Remember to undo the last forward operation first!)

• Add 13 to both sides.

• Multiply both sides by 3/2.

 $\frac{2}{3}\left(x-13\right)=22$  

Multiply both sides by the reciprocal of 2/3.
 $\left(\frac{3}{2}\right)\frac{2}{3}\left(x-13\right)=22\left(\frac{3}{2}\right)$  

 $x-13=33$  

Multiple Choice

What is the next step we would take to solve the equation?

 $x-13=33$  

• Add 13 to both sides.

• Subtract 13 from both sides.

 $\frac{2}{3}\left(x-13\right)=22$  

Multiply both sides by the reciprocal of 2/3.
 $\left(\frac{3}{2}\right)\frac{2}{3}\left(x-13\right)=22\left(\frac{3}{2}\right)$  

 $x-13=33$  

    $+13\ \ \ \ +13$  Add 13 to both sides.

 $x=46$  

Check your work

 $\frac{2}{3}\left(x-13\right)=22$  

Plug in 46 for x.
 $\frac{2}{3}\left(46-13\right)=?$  

 $\frac{2}{3}\left(33\right)=?$  

 $\frac{2}{3}\times\frac{33}{1}=\frac{66}{3}=22$  Correct!

Solve these on a separate piece of paper.

Be sure to check your work!

•  $-4c-4=8$  

•  $-7\left(6+d\right)=49$ 

•  $\frac{1}{4}\left(w-3\right)=-15$  

•  $4t+3.5=12.5$ 

Poll

On a scale of 1 to 5, how would you rate your understanding of how to solve two-step equations?

1 - I do not understand ANYTHING we talked about today.

2 - I understand a little but I know I need more help.

3 - I understand the basic idea, but I know I need more practice.

4 - I understand the concept but need to practice a little more in order to master it.

5 - I got this!

• 1 - I do not understand ANYTHING we talked about today.

• 2 - I understand a little but I know I need more help.

• 3 - I understand the basic idea, but I know I need more practice.

• 4 - I understand the concept but need to practice a little more in order to master it.

• 5 - I got this!