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1-9 Solving Two-Step Equations
Preview
Evaluating Algebraic Expressions
Warm Up
California Standards
Lesson Presentation
1-9 Solving Two-Step Equations
Warm Up
AddEvaluating
or subtract.Algebraic Expressions
1. –6 + (–5) –11
2. 4 – (–3)
7
3. –2 + 11
9
Multiply or divide.
4. –5(–4)
20
5. 18
–3
6. 7(–8)
–6
–56
1-9 Solving Two-Step Equations
Evaluating
Algebraic Expressions
California
Standards
AF4.1 Solve two-step linear
equations and inequalities in one variable
over the rational numbers, interpret the
solution or solutions in the context from
which they arose, and verify the
reasonableness of the results.
Also covered: AF1.1
1-9 Solving Two-Step Equations
Evaluating
Algebraic
Two-step
equations
contain two Expressions
operations.
For example, the equation 6x  2 = 10
contains multiplication and subtraction.
Multiplication
6x  2 = 10
Subtraction
1-9 Solving Two-Step Equations
Additional Example 1A: Translating Sentences into
Two-Step Equations
Evaluating Algebraic Expressions
Translate the sentence into an equation.
17 less than the quotient of a number x and 2
is 21.
17 less than the quotient of a number x and 2 is 21.
(x ÷ 2) – 17 = 21
x  17 = 21
2
1-9 Solving Two-Step Equations
Additional Example 1B: Translating Sentences into
Two-Step Equations
Evaluating Algebraic Expressions
Translate the sentence into an equation.
Twice a number m increased by –4 is 0.
Twice a number m increased by –4 is 0.
2 ● m + (–4) = 0
2m + (–4) = 0
1-9 Solving Two-Step Equations
Check It Out! Example 1A
Translate
the sentence
into an Expressions
equation.
Evaluating
Algebraic
7 more than the product of 3 and a number t
is 21.
7 more than the product of 3 and a number t is 16.
3 ● t + 7 = 16
3t + 7 = 16
1-9 Solving Two-Step Equations
Check It Out! Example 1B
Translate
the sentence
into an Expressions
equation.
Evaluating
Algebraic
3 less than the quotient of a number x and 4
is 7.
3 less than the quotient of a number x and 4 is 7.
(x ÷ 4) – 3 = 7
x 3=7
4
1-9 Solving Two-Step Equations
Additional Example 2A: Solving Two-Step
Equations Using Division
Evaluating Algebraic Expressions
Solve 3x + 4 = –11.
Step 1:
3x + 4 = –11
–4 –4
3x
= –15
Step 2:
3x = –15
3
3
x = –5
Note that x is multiplied by
3. Then 4 is added. Work
backward: Since 4 is added
to 3x, subtract 4 from both
sides.
Since x is multiplied by 3,
divide both sides by 3 to
undo the multiplication.
1-9 Solving Two-Step Equations
Additional Example 2B: Solving Two-Step
Equations Using Division
Evaluating Algebraic Expressions
Solve 8 = –5y – 2.
8 = –5y – 2
+2
+2
Since 2 is subtracted from
–5y, add 2 to both sides to
undo the subtraction.
10 = –5y
10 = –5y
–5
–5
–2 = y or
y = –2
Since y is multiplied by –5,
divide both sides by –5 to
undo the multiplication.
1-9 Solving Two-Step Equations
Check It Out! Example 2A
Evaluating
Algebraic
Solve
7x + 1 = –13.
Step 1:
7x + 1 = –13
–1
–1
7x
Step 2:
= –14
7x = –14
7
7
x = –2
Expressions
Note that x is multiplied by
7. Then 1 is added. Work
backward: Since 1 is added
to 7x, subtract 1 from both
sides.
Since x is multiplied by 7,
divide both sides by 7 to
undo the multiplication.
1-9 Solving Two-Step Equations
Check It Out! Example 2B
Evaluating
Algebraic
Solve
12 = –5y – 3.
12 = –5y – 3
+3
+3
15 = –5y
15 = –5y
–5
–5
–3 = y or
y = –3
Expressions
Since 3 is subtracted from
–5y, add 3 to both sides to
undo the subtraction.
Since y is multiplied by –5,
divide both sides by –5 to
undo the multiplication.
1-9 Solving Two-Step Equations
Additional Example 3A: Solving Two-Step Equations
Using Multiplication
Evaluating Algebraic Expressions
Solve 4 + m = 9.
7
Note that m is divided by 7.
Step 1:
4+ m = 9
7
Then 4 is added. Work
–4
–4
backward: Since 4 is added
m = 5
to m , subtract 4 from both
7
7
sides.
Step 2:
(7) m = 5(7) Since m is divided by 7,
7
multiply both sides by 7 to
undo the division.
m = 35
1-9 Solving Two-Step Equations
Additional Example 3B: Solving Two-Step
Equations Using Multiplication
Evaluating Algebraic Expressions
Solve 14 = z – 3.
2
Since 3 is subtracted from
Step 1:
14 = z – 3
12
tz , add 3 to both sides to
+3
+3
2
undo the subtraction.
17 = z
2
Step 2: (2)17 = z (2)
2
34 = z
z is divided by 2, multiply
both sides by 2 to undo
the division.
1-9 Solving Two-Step Equations
Check It Out! Example 3A
Evaluating
Solve
2 + k = 9. Algebraic Expressions
6
Note that k is divided by 6.
Step 1:
2+ k = 9
6
Then 2 is added. Work
–2
–2
backward. Since 2 is added
k = 7
to k , subtract 2 from both
6
6
sides.
k = 7(6) Since k is divided by 6,
(6)
Step 2:
6
multiply both sides by 6 to
undo the division.
k = 42
1-9 Solving Two-Step Equations
Check It Out! Example 3B
Evaluating
Solve
10 = p – 2. Algebraic Expressions
4
Since 2 is subtracted from
Step 1:
10 = p – 2
14
tp , add 2 to both sides to
+2
+2
4
undo the subtraction.
12 = p
4
Step 2: (4)12 = p (4)
4
48 = p
p is divided by 4, multiply
both sides by 4 to undo
the division.
1-9 Solving Two-Step Equations
Additional Example 4: Consumer Math Application
Donna buys a portable DVD player that costs
Evaluating Algebraic Expressions
$120. She also buys several DVDs that cost
$14 each. She spends a total of $204. How
many DVDs does she buy?
Let d represent the number of DVDs that Donna
buys. That means Donna can spend $14d plus the
cost of the DVD player.
cost of DVD +
player
$120
+
cost of
DVDs
=
total cost
14d
=
$204
1-9 Solving Two-Step Equations
Additional Example 4 Continued
Donna buys a portable DVD player that costs
Evaluating Algebraic Expressions
$120. She also buys several DVDs that cost
$14 each. She spends a total of $204. How
many DVDs does she buy?
$120
+
14d
=
$204
120 + 14d = 204
–120
–120
14d = 84
14d = 84
14
14
d=6
Donna purchased 6 DVDs.
1-9 Solving Two-Step Equations
Check It Out! Example 4
John buys an MP3 player that costs $249. He
Evaluating Algebraic Expressions
also buys several songs that cost $0.99 each.
He spends a total of $277.71. How many
songs does he buy?
Let s represent the number of songs that John
buys. That means John can spend $0.99s plus the
cost of the MP3 player.
cost of MP3
player
+
cost of
songs
=
total cost
$249
+
0.99s
=
$277.71
1-9 Solving Two-Step Equations
Check It Out! Example 4 Continued
John buys an MP3 player that costs $249. He
Evaluating Algebraic Expressions
also buys several songs that cost $0.99 each.
He spends a total of $277.71. How many
songs does he buy?
$249
+
0.99s
=
$277.71
249 + 0.99s = 277.71
–249
–249
0.99s = 28.71
0.99s = 28.71
0.99
0.99
s = 29
John purchased 29 songs.
1-9 Solving Two-Step Equations
Lesson Quiz
Translate the sentence into an equation.
Evaluating Algebraic Expressions
1. The product of –3 and a number c, plus 14, is –7.
–3c + 14 = –7
Solve.
2. 17 = 2x – 3 10
3. –4m + 3 = 15
x
4. w – 5 = 1 12
5. 2 = 3 –
4
2
6. A discount movie pass costs $14. With
pass, movie tickets cost $6 each. Fern
–3
4
the
spent
a total of $68 on the pass and movie tickets.
How many movies did he see? 9