This document contains examples of solving equations with steps shown. It includes:
1) Five examples of solving equations of the form p(x+q)=r, showing the steps of writing the equation, using properties of equality to isolate the variable, and checking the solution.
2) An example of writing and solving an equation to find an unknown amount based on contextual information.
3) Questions asking how the content can help understand what it means for two quantities to be equal.
1. Solve each equation. Check your solution.
1. 4x + 8 = 32
2. 15 β 3a = 45
3. β9 + 7x = 68
4. β18 = β2m β 68
5. Four less than six times a number n is 32. Write and
solve an equation to find the number.
Course 2, Lesson 6-5
2. Course 2, Lesson 6-5
ANSWERS
1. x = 6
2. a = β10
3. x = 11
4. m = β25
5. 6n β 4 = 32; n = 6
3. WHAT does it mean to say
two quantities are equal?
Expressions and Equations
Course 2, Lesson 6-5
6. β’ To solve two-step equations in the
form p(x + q) = r
β’ To solve equations in the form
p(x + q) = r with rational coefficients
Course 2, Lesson 6-5
Expressions and Equations
7. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. Solve 3(x + 5) = 45.
Write the equation.3(x + 5) = 45
Division Property of Equality
β 5 = β 5
Simplify.x + 5 = 15
Subtraction Property of Equality
x = 10
=
Solve arithmetically.
Draw a bar diagram. From the diagram,
you can see that x + 5 = 45 Γ· 3 or 15.
So, x = 15 β 5 or 10.
Solve algebraically.
Simplify.
13. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. Solve 0.2(c β 3) = β10. Check your solution.
Write the equation.0.2(c β 3) = β10
Division Property of Equality
Simplify.
Addition Property of Equality
Simplify.
c β 3 = β50
Check 0.2(c β 3) = β10 Write the original equation.
?
The sentence is true.
Replace c with β 47.
Is this sentence true?
+3 = + 3
c = β47
0.2( β47 β 3) = β10
β10 = β10
15. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
5. Jamal and two cousins received the same amount of money
to go to a movie. Each boy spent $15. Afterward, the boys
had $30 altogether. Write and solve an equation to find the
amount of money each boy received.
Write the equation.
Let m represent the amount of money each boy received.
Simplify.
Addition Property of Equality
Simplify.
m β 15 = 10
So, each boy received $25.
3(m β 15) = 30
Division Property of Equality
+15 +15
m = 25
16. Answer
Need Another Example?
Javier bought 3 bags of balloons for a party. He used
8 balloons from each bag. Write and solve an equation
to find how many balloons were originally in each bag
if there were 21 balloons left over.
3(b β 8) = 21; 15 balloons
17. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-5
Expressions and Equations
18. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-5
Expressions and Equations
Sample answers:
β’ To solve two-step equations, such as 3(x + 2) = 9
β’ To solve two-step equations, such as (x + 2) = 9
1
3
19. The side length s + 3 of a square
with a perimeter of 52 inches
can be found using the equation
4(s + 3) = 52. What is the
side length of the square?
Ratios and Proportional RelationshipsExpressions and Equations
Course 2 Lesson 6-5