Title: Lesson 9-2
Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 2-7

For Examples 1-2 Solve One-Step Equations
Solve each equation. Check your solution.
a.  x + 6 = 11.

METHOD 1  Use models.	METHOD 2  Use symbols.

Subtract 6 from each side to “undo” the addition of 6 on the left.

Model the equation.	x + 6 = 11	Write the equation.

x + 6 =   11
   − 6 =  − 6		
x       =     5      11 − 6 = 5

Remove 6 counters from each side.	

The solution is 5.

b. m + 4 = 2

METHOD 1  Use models.	METHOD 2  Use symbols.	

Subtract 4 from each side to undo m + 4.

Model the equation.	m + 4 = 2	Write the equation.

m + 4 =     2
    − 4 =  − 4	Subtract 4 from each side.	
m       =   −2	2 − 4 = −2 

Check
  m + 4 = 2	Write the equation.
−2 + 4  2	Replace m with −2.
         2 = 2 ✓	This sentence is true.

Add 2 zero pairs to the right side 
so there are 4 positive counters.

Remove 4 positive counters from 
each side.

The solution is −2.

c.  x – 5 = 3

METHOD 1  Use models.	 METHOD 2  Use symbols.

Model the equation. 	x − 5 = 3	Write the equation.

Add 5 to each side to undo the subtraction of 5 on the left.

 x − 5 =     3
    + 5 =  + 5	Add 5 to each side.	
 x       =     8	Simplify.

Add 5 positive counters to each side 
of the mat. Remove the zero pairs.

The solution is 8.

d. k − 3 = −9

Check    k − 3 = −9	
           −6 − 3  −9	
                 −9 = −9 ✓

k – 3 =   − 9	Write the equation.
   + 3 =   + 3		Use the inverse of subtraction. Add 3 to each side.	
d      =    −6	Simplify.

The solution is −6.

e. 6x = 18 

Model the equation.

					

Divide the 18 counters equally into 6 groups. 
There are 3 in each group.

Check    6x = 18	Write the original equation.	
            6(3)  18	Replace x with 3.	
               18 = 18 	This sentence is true. ✓

The solution is 3.

f. −4x = 24

 −4x = 24	Write the equation.	
  (−4x)/(−4) = 24/(−4)	Use the inverse of multiplication. Divide each side by −4.
   1x = −6	−4 ÷ (−4) = 1, 24 ÷ (−4) = −6
     x = −6	1x = x

Check    -4x = 24	Write the original equation.	
            -4(-6)  24	Replace x with -6.	
               24 = 24 	This sentence is true. ✓

The solution is -6.

For Examples 3-4 Solve Two-Step Equations

g. Solve 5x + 4 = 34.
	5x + 4 	= 34	Multiplication and addition are used.
	5x + 4 – 4	= 34 – 4	First, use the inverse of addition.
	5x	= 30		Subtract 4 from each side.
	(5x) ÷ 5 	= 30 ÷ 5	Then, use the inverse of multiplication. 
	x	= 6		Divide each side by 5. 

Check:	5(6) + 4 	= 34
		30 + 4	= 34
		34	= 34 √

For Example 5 
h. [Real-World Example] ANIMALS The world’s biggest reptile is the saltwater crocodile, which weighs 1,150 pounds on average. This is 650 pounds more than the average weight of the world’s largest snake, the anaconda. Write and solve an addition equation to find the weight of an average anaconda.

Words

Variable

Equation

650 pounds plus the weight of an average anaconda 
 is 1,150 pounds.

Let w represent the weight of an average anaconda.

	650    + 	w 	= 1,150

   650 + w = 1,150	Write the equation.
− 650       	= − 650	Subtract 650 from each side.
	w =    500	1,150 − 650 = 500

So, an average anaconda weighs 500 pounds.