Here is a two-step equation example with steps to solve it:
2x + 3 = 11
Subtract 3 from both sides using the subtraction property of equality:
2x + 3 - 3 = 11 - 3
2x = 8
Divide both sides by 2 using the division property of equality:
2x/2 = 8/2
x = 4
To solve a two-step equation:
1) Use addition or subtraction to isolate the variable term on one side of the equation.
2) Use multiplication or division to solve for the variable.
By applying the properties of equality, this allows you to transform the original equation into an equivalent equation where the variable term is alone
1. Course 3, Lesson 2-2
Solve each equation. Check your solution.
1. = 6
2. 0.6y = −12
3. =
4. 8.6n = −365.5
5. For art class, each student is going to make a piñata using
pound of paste. The art teacher bought 20 pounds of
paste. Write and solve an equation that can be used to
determine the number of students that can make a piñata.
4
5
3
4
n
1
2
2
x
1
22
2
8. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
1. Solve 2x + 3 = 7.
There are two 1-tiles in each group, so x = 2.
Write the equation.
Subtraction Property of Equality
Division Property of Equality
Remove three 1-tiles from each mat.
Separate the remaining tiles into 2 equal groups.
Using either method, the solution is 2.
7
Use a model.
2x + 3 – 3 = 7 – 3
2x = 4
Use symbols.
2x + 3 = 7
Simplify.x = 2.
–3 = –3
2x = 4
10. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
2. Solve 25 = n – 3.
Write the equation.
Addition Property of Equality
Multiplication Property of Equality
25 = n – 3
28 = n
The solution is 112.
112 = n
Simplify.
+3 = +3
14. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
4. Chicago’s lowest recorded temperature in degrees
Fahrenheit is –27°. Solve the equation –27 = 1.8C + 32 to
convert to degrees Celsius.
Write the equation.
Division Property of Equality
–32.8 ≈ C
Simplify.
Subtraction Property of Equality
–27 = 1.8C + 32
Simplify. Check the solution.
So, Chicago’s lowest recorded temperature is about
–32.8 degrees Celsius.
–32 = –32
–59 = 1.8C
15. Answer
Need Another Example?
Melisa wants to put trim molding around a
rectangular table. The table is 45 inches long and
she has 150 inches of trim. Solve the equation
150 = 2w + 90 to find the width of the table.
30 in.
16. How did what you learned
today help you answer the
WHAT is equivalence?
Course 3, Lesson 2-2
Expressions and Equations
17. How did what you learned
today help you answer the
WHAT is equivalence?
Course 3, Lesson 2-2
Expressions and Equations
Sample answers:
• In order to maintain the equality, when you perform an
operation on one side of an equation, you must
perform the same operation on the other side of the
equation.
• Equations are equivalent when they have the same
solution.
18. Write a two-step equation
and explain how to solve it.
Ratios and Proportional RelationshipsExpressions and Equations
Course 3, Lesson 2-2