Two Step Equations

Two Step Equations

Our Goal

• Isolate the variable on one side of the equal sign

Multiple Choice

What does isolate the variable mean?

• Get the variable alone

• Get rid of the variable

Our Strategy

• Keep it balanced

• What you do to one side, do to the other

• "Copy and Paste"

Use Inverse Operations to isolate the variable

• Inverse of addition - subtraction

• Inverse of subtraction - addition

• Inverse of multiplication - division

• Inverse of division - multiplication

Multiple Choice

What is the inverse of multiplication?

• Addition

• Subtraction

• Multiplication

• Division

3x - 6 = 12

• Add 6 to both sides: 3x = 18

• Divide both sides by 3: x = 6

• Check: 3(6) - 6 = 18 - 6 = 12

 $15\ =\ 4y\ +\ 5$  
 $-5\ \ \ \ \ \ \ \ \ \ \ \ -5$  
 $10\ =\ 4y$  
 $\div4\ \ \ \ \ \div4$  
 $2.5\ =\ y$  

Check:  4(2.5) + 5 = 10 + 5 = 15

Multiple Choice

12g - 5 = 19

Which is the correct 1st step?

• Add 12 to both sides

• Add 5 to both sides

• Add 19 to both sides

Multiple Choice

 $12g-5=19$  

 $\ \ \ \ \ \ \ +5\ \ \ \ +5\ \ \ \ \ \ \ \$  
 $12g\ \ \ \ \ \ \ =\ 24$  
What is the next step?

• Multiply both sides by 12

• Divide both sides by 12

• Multiply both sides by 24

• Divide both sides by 24

 $12g=24$  

 $\div12\ \div12$  
 $\ \ \ g\ =\ 2$   

Multiple Choice

2t -7 = 3

Find the value of t

• -2

• 2

• 5

• 20

Multiple Choice

What is the reciprocal of  $\frac{2}{5}$  

•  $-\ \frac{2}{5}$  

• 0.4

•  $\frac{5}{2}$  

 $\frac{2}{5}\ \cdot\ \frac{5}{2}$  

•  $\frac{10}{10}$  

• 1 in disguise!

• Multiplicative Inverse:  When you multiply a fraction in n/d form by its RECIPROCAL you will always get 1

• If the coefficient in your algebraic equation is a fraction - MULTIPLY by the reciprocal!

Multiple Choice

 $\frac{2}{5}\ h\ +\ 6\ =\ 8$  


What is the first step that should be done to both sides?

• +6

• -6

• +8

• -8

Multiple Choice

 $\frac{2}{5}\ h\ =\ 2$  


What is the second step that should be done to both sides? 

•  $+\ \frac{5}{2}$  

•  $-\ \frac{5}{2}$  

•  $\cdot\ \frac{5}{2}\$  

•  $\div\ \frac{5}{2}$  

Multiple Choice

 $\frac{2}{5}\ h\ =\ 2$  

What is the value of h?

•  $\frac{4}{5}$  

•  $2\ \frac{2}{5}$  

• 2

• 5

 $\frac{2}{5}\ h\ +\ 6\ =\ 8$  
  $\ \ \ \ \ \ \ -6\ \ \ \ \ -6$  
 $\frac{2}{5}\ h\ \ \ \ \ \ \ \ \ \ =\ 2$  

 $\frac{5}{2}\cdot\frac{2}{5}\ \cdot\ h\ \ =\ \frac{2}{1}\cdot\frac{5}{2}$  

 $\frac{10}{10}\ \cdot\ h\ \ =\ \frac{10}{2}$  

 $h\ =\ 5$  

Multiple Choice

10 = 2d - 5

What is the value of d?

• 2.5

• 7.5

• 15

• 20

Multiple Choice

 $\frac{2}{3}x\ +\ 1\ =\ \frac{5}{3}$  

What is the value of x?

• 0

• 1

• 2

• 3