Transcript 2 Step Equations - Caldwell County Schools

10-1 Solving Two-Step Equations
Warm Up
Problem of the Day
Lesson Presentation
Course 3
10-1 Solving Two-Step Equations
Warm Up
Solve.
1. x + 12 = 35 x = 23
2. 8x = 120
x = 15
3. y = 7
y = 63
9
4. –34 = y + 56 y = –90
Course 3
10-1 Solving Two-Step Equations
Problem of the Day
x is an odd integer. If you triple x and
then subtract 7, you get a prime
number. What is x? (Hint: Think about
what the prime number must be in
order for x to be an odd.)
x=3
Course 3
10-1 Solving Two-Step Equations
Learn to solve two-step equations.
Course 3
10-1 Solving Two-Step Equations
Sometimes more than one inverse operation
is needed to solve an equation. Before
solving, ask yourself, “What is being done to
the variable, and in what order?” Then work
backward to undo the operations.
Course 3
10-1 Solving Two-Step Equations
Additional Example 1: Problem Solving Application
The mechanic’s bill to repair Mr. Wong’s
car was $650. The mechanic charges
$45 an hour for labor, and the parts that
were used cost $443. How many hours
did the mechanic work on the car?
Course 3
10-1 Solving Two-Step Equations
Additional Example 1 Continued
1
Understand the Problem
List the important information:
The answer is the number of hours the
mechanic worked on the car.
• The parts cost $443.
• The labor cost $45 per hour.
• The total bill was $650.
Let h represent the hours the mechanic
worked.
Total bill =
Parts
+
Labor
650
=
443
+
45h
Course 3
10-1 Solving Two-Step Equations
Additional Example 1 Continued
2
Make a Plan
Think: First the variable is multiplied by
45, and then 443 is added to the result.
Work backward to solve the equation.
Undo the operations in reverse order:
First subtract 443 from both sides of the
equation, and then divide both sides of
the new equation by 45.
Course 3
10-1 Solving Two-Step Equations
Additional Example 1 Continued
3
Solve
650 = 443 + 45h
–443 –443
207 =
207 = 45h
45
45
Subtract to undo the addition.
45h
Divide to undo multiplication.
4.6 = h
The mechanic worked for 4.6 hours on
Mr. Wong’s car.
Course 3
10-1 Solving Two-Step Equations
Additional Example 1 Continued
4
Look Back
If the mechanic worked 4.6 hours, the labor
would be $45(4.6) = $207. The sum of the
parts and the labor would be $443 + $207 =
$650.
Course 3
10-1 Solving Two-Step Equations
Try This: Example 1
The mechanic’s bill to repair your car
was $850. The mechanic charges $35
an hour for labor, and the parts that
were used cost $275. How many
hours did the mechanic work on your
car?
Course 3
10-1 Solving Two-Step Equations
Try This: Example 1 Continued
1
Understand the Problem
List the important information:
The answer is the number of hours the
mechanic worked on your car.
• The parts cost $275.
• The labor cost $35 per hour.
• The total bill was $850.
Let h represent the hours the mechanic worked.
Total bill =
Parts
+
Labor
850
=
275
+
35h
Course 3
10-1 Solving Two-Step Equations
Try This: Example 1 Continued
2
Make a Plan
Think: First the variable is multiplied by 35,
and then 275 is added to the result. Work
backward to solve the equation. Undo the
operations in reverse order: First subtract
275 from both sides of the equation, and
then divide both sides of the new equation by
35.
Course 3
10-1 Solving Two-Step Equations
Try This: Example 1 Continued
3
Solve
850 = 275 + 35h
–275 –275
575 =
575 = 35h
35
35
Subtract to undo the addition.
35h
Divide to undo multiplication.
16.4  h
The mechanic worked for about 16.4 hours on your
car.
Course 3
10-1 Solving Two-Step Equations
Try This: Example 1 Continued
4
Look Back
If the mechanic worked 16.4 hours, the
labor would be $35(16.4) = $574. The sum
of the parts and the labor would be $275 +
$574 = $849.
Course 3
10-1 Solving Two-Step Equations
Additional Example 2A: Solving Two-Step Equations
Solve.
n
A.
+ 7 = 22
3
Think: First the variable is divided by 3, and
then 7 is added. To isolate the variable, subtract
7, and then multiply by 3.
n + 7 = 22
3
–7 –7
Subtract to undo addition.
n
= 15
3
n
Multiply to undo division.
3  = 3  15
3
n = 45
Course 3
10-1 Solving Two-Step Equations
Additional Example 2A Continued
Check n + 7 = 22
3
?
45 + 7 =
22
3
?
15 + 7 = 22 
Course 3
Substitute 45 into the
original equation.
10-1 Solving Two-Step Equations
Additional Example 2B: Solving Two-Step Equations
B. 2.7 = –1.3m + 6.6
Think: First the variable is multiplied by –1.3, and
then 6.6 is added. To isolate the variable, subtract
6.6, and then divide by –1.3.
2.7 = –1.3m + 6.6
–6.6
–6.6
–3.9 = –1.3m
Subtract to undo addition.
–3.9 = –1.3m
–1.3
–1.3
Divide to undo multiplication.
3=m
Course 3
10-1 Solving Two-Step Equations
Additional Example 2C: Solving Two-Step Equations
C. y – 4 = 9
3
Think: First 4 is subtracted from the variable, and
then the result is divided by 3. To isolate the
variable, multiply by 3, and then add 4.
y – 4= 9
3
3 · y 3– 4 = 3 · 9
y – 4 = 27
+4 +4
y = 31
Course 3
Multiply to undo division.
Add to undo subtraction.
10-1 Solving Two-Step Equations
Try This: Example 2A
Solve.
n
A.
+ 5 = 29
4
Think: First the variable is divided by 4, and
then 5 is added. To isolate the variable, subtract
5, and then multiply by 4.
n + 5 = 29
4
–5 –5
4

n
=4
4

n = 96
Course 3
Subtract to undo addition.
24
Multiply to undo division.
10-1 Solving Two-Step Equations
Try This: Example 2A Continued
Check n + 5 = 29
4
?
96 + 5 =
29
4
?
24 + 5 = 29 
Course 3
Substitute 96 into the
original equation.
10-1 Solving Two-Step Equations
Try This: Example 2B
B. 4.8 = –2.3m + 0.2
Think: First the variable is multiplied by –2.3, and
then 0.2 is added. To isolate the variable, subtract
0.2, and then divide by –2.3.
4.8 = –2.3m + 0.2
–0.2
–0.2
4.6 = –2.3m
Subtract to undo addition.
4.6 = –2.3m
–2.3
–2.3
Divide to undo multiplication.
–2 = m
Course 3
10-1 Solving Two-Step Equations
Try This: Example 2C
C. y – 2 = 8
4
Think: First 2 is subtracted from the variable, and
then the result is divided by 4. To isolate the
variable, multiply by 4, and then add 2.
y – 2= 8
4
4 · y 4– 2 = 4 · 8
y – 2 = 32
+2 +2
y = 34
Course 3
Multiply to undo division.
Add to undo subtraction.
10-1 Solving
Insert Lesson
Two-Step
Title
Equations
Here
Solve.
Lesson Quiz
1. x – 3 = 10 x = –117
–9
2. 7y + 25 = –24 y = –7
3. –8.3 = –3.5x + 13.4 x = 6.2
4. y + 5 = 3 y = 28
11
5. The cost for a new cell phone plan is $39 per
month plus a one-time start-up fee of $78. If you
are charged $1014, how many months will the
contract last? 24 months
Course 3