Download Lesson 5: Solving Two

Chapter 3 Lesson 5
Solving 2-Step Equations
Pgs. 120-124
What you will learn:
To solve 2-step equations!
Background
A two step equation contains two operations.
In the equation 2x + 1 = 9, x is multiplied by 2
and then 1 is added. To solve two-step equations,
use inverse operations to undo each operation in
reverse order. You can solve 2x + 1 = 9 in two
steps.
Step 1: First, undo addition
2x + 1 = 9
2x + 1 -1 = 9 -1
Subtract 1 from each side
2x = 8
Step 2: Undo the multiplication
2x = 8
2x = 8
2 2
x=4
How do you do the check
of 2x + 1 = 9 if x = 4?
Replace the x with 4 in the ORIGINAL
Problem and solve step by step.
2(4) + 1 = 9
8+1=9
9=9
This problem checks out!
Solve a two-step equation and
check the solution.
5x - 2 = 13
Step 1: Undo the subtraction.
5x - 2 +2 = 13 +2
5x = 15
Step 2: Undo the multiplication
5x = 15
5x = 15
5
5
x=3
Check: 5x - 2 = 13
5(3) - 2 = 13
15 - 2 = 13
13 = 13 
Solve the equation and check
the answer.
4 = n + 11
6
What do you do first?
Undo the addition
4 - 11 = n + 11 -11
6
-7 = n
6
What do you do next?
-7(6) = n (6)
6
-42 = n
Undo the division
Now check your answer
In the original problem.
4 = n + 11
6
4 = -42 + 11
6
4 = -7 + 11
4=4
Remember, in order for a check to work
out, both sides of the equation need
to equal the same!!
Solve an equation with
Negative coefficients
4 - x = 10
Think of the problem as 4 - 1x = 10
4 - 4 - 1x = 10 - 4
-1x = 6
-1x = 6
-1
-1
x = -6
Check: 4 - x = 10
4 - (-6) = 10
10 = 10 
Combine Like Terms before
solving
m - 5m + 3 = 47 Remember it can be rewritten
as m + (-5m) + 3 = 47
Combine like terms:
m - 5m + 3 = 47
-4m + 3 = 47
Subtract 3 from each side: -4m + 3 - 3 = 47 - 3
Simplify:
-4m = 44
Divide both sides by -4:
-4m = 44
-4
-4
Simplify:
m = -11
Check: m - 5m + 3 = 47
-11 - 5(-11) + 3 = 47
-11 + 55 + 3 = 47
44 + 3 = 47
47 = 47 
Use an equation to solve a
problem
A telephone calling card allows for 25¢ per
minute plus a one-time service charge of 75¢. If the
total cost of the card is $5, solve 25m + 75 = 500 to
find the number of minutes you can use the card.
Step 1: Undo the addition
25m + 75 -75 = 500 -75
25m = 425
Step 2: Undo the multiplication
25m = 425
25
25
m = 17
Check:
25(17) + 75 = 500
425 + 75 = 500
500 = 500 
You try. Look at the questions
Carefully!
Check:
3(3) + 4 = 13
3y + 4 = 13
9 + 4 = 13
3y + 4 -4 = 13 - 4
13 = 13 
3y = 9
3y = 9
y=3
3
3
20 - z = 11
20 - 20 - z = 11 - 20
20 - 9 = 11
-z = -9
11 = 11 
-z = -9
-1
-1
z=9
3n + n - 4 = 12
3(4) + 4 - 4 = 12
4n - 4 + 4 = 12 + 4
12 = 12 
4n= 16
4n = 16
4
4
n=4