Transcript Lesson 3.1 Solving Two-Step Equations

Chapter 3
Multi-Step Equations
and
Inequalities
Chapter Prerequisite Skills
Chapter Prerequisite Skills
1. Explain what an expression is and what an
equation is. Then give one example.
An expression can be a variable expression or a
numerical expression. It is not equal or compared
to anything. 2x + 7 or 28 – 7
An equation is a mathematical sentence comparing
two expressions. 2x + 7 = 28 – 7
Use the distributive property to write and equivalent
variable expression.
2. 9(x – 4) 9x - 36
4. -6(-m + 12) 6m – 72
3. 8(z – 7) 8z – 56
5. -10(n – 5) -10n + 50
Chapter Prerequisite Skills
Simplify the Expression.
6. c + 4 – c 4
8. 4(a + 2) + a 5a + 8
7. 9b – 12b + 3 -3b + 3
9. 2(2d + 5 + d) 6d +10
Solve the equation. Check the solution.
10. x + 13 = 7 -6
12. q – 9.6 = 2 11.6
11. h ÷ 6 = -8 -48
13. 65 = -13b -5
Lesson 3.1
Solving Two-Step Equations
Skill Check
Lesson Presentation
Lesson Quiz
Skill Check
1. -44 – 88 = -132
2. -77 + 37 = -40
3. -270 ÷ -4 = 67.5
4. 765 • (1 ÷ 765) = 1
Writing Variable Expressions You can solve a real-world problem by
creating a verbal model and using it to write a variable expression. A verbal
model describes a problem using words as labels and using math
symbols to relate the words. The table shows common words and phrases
that indicate mathematical operations.
Common Words and Phrases that Indicate Operations
Addition
Subtraction
Multiplication
Division
plus
the sum of
increased by
total
more than
added to
minus
the difference of
decreased by
fewer than
less than
subtracted from
times
the product of
multiplied by
of
divided by
divided into
the quotient of
Study Strategy
When you solve an equation show every step
when solving, because these steps are important
for diagnosing errors.
For example: 3x + 7 = -5
Subtract 7 from both sides: -7 + 3x + 7 = -5 – 7
Simplify: 3x = -12
Divide each side by 3: 3x ÷ 3 = -12 ÷ 3
Simplify: x = -4
EXAMPLE
1
Using Subtraction and Division to Solve
Solve.
a. 8x + 7 = 47
b. 1 = 2r + 9
c. 2 = 6h + 20
SOLUTION
a. 8x + 7 = 47
b. 1 = 2r + 9
c. 2 = 6h + 20
-7 + 8x + 7 = 47 - 7
8x = 40
-9 + 1 = 2r + 9 – 9
-8 = 2r
-20 + 2 = 6h + 20 – 20
-18 = 6h
8x/ 8 = 40/ 8
-8/2 = 2r/2
-18/6 = 6h/6
x = 5
r = -4
h = -3
EXAMPLE
2
Using Addition and Multiplication to Solve
Solve.
a. y/4 – 2 = 1
b. 2 = d/5 - 1
c. 12 = f/2 – 8
SOLUTION
b. 2 = d/5 - 1
c. 12 = f/2 – 8
2 + y/4 – 2 = 1 + 2
y/4 = 3
1 + 2 = d/5 – 1 + 1
3 = d/5
8 + 12 = f/2 – 8 + 8
20 = f/2
4(y/4) = (3)4
5(3) = (d/5)5
2(20) = (f/2)2
y = 12
d = 15
f = 40
a. y/4 – 2 = 1
EXAMPLE
3
Solving an Equation with Negative Coefficients
Solve.
a. 9 – 6a = 45
b. 6 – 2m = 8
c. -2 = 5 – n
SOLUTION
b. 6 – 2m = 8
c. -2 = 5 – n
-9 + 9 – 6a = 45 – 9
– 6a = 36
-6 + 6 – 2m = 8 – 6
– 2m = 2
-5 – 2 = 5 – n – 5
-7 = -n
– 6a/-6 = 36/-6
– 2m/-2 = 2/-2
-7/-1 = -n/-1
a = -6
m = -1
n = 7
a. 9 – 6a = 45
4 Writing and Solving a Two-Step Equation
Motorcycle William makes a down payment of 1,100,000
won on a motorcycle costing 2,300,000 won. If no interest is
charged, how many monthly payments of 150,000 won must
he make until he has finished paying for the motorcycle? Let
p represent the number of monthly payments. Write a verbal
model.
EXAMPLE
SOLUTION
Amount of
down payment
+
Monthly
Payment
•
Number of monthly
payments, p
=
Total Cost of
Motorcycle
1100000 + 150000 • p = 2300000
– 1100000 + 1100000 + 150000p = 2300000 - 1100000
150000p = 1200000
150000p/150000 = 1200000/150000
p=8
ANSWER
William must make 8 monthly payments of 150000 won.
Lesson Quiz
Solve the equation.
1. 9b + 8 = 80
b = 8
2. z/7- 5 = -3
z = 14
3. -10 = 20 – 6c c = 5
4. 11 – b/6 = 23 b = -72
5. Challenge Solve (8 + k)/5 = 3
k = 7
Closure
• 1.) Explain how you solve the equation
11 – 4p = -1?
• 2.) Asia girl has lived one fourth of her
life in S.Korea, one fifth of her life in
Thailand, one third of her life in China,
and she has been living in Japan for the
past 13 years. How old is Asia girl?
Asia girl is 60 years old. 
Lesson 3.1 Homework:
pp.122-124 Exs. (1, 20, 22, 24, 26,
28, 30, 32, 34, 35abc, 45, 46)
Challenge/Bonus 36