10-3 solving two-step equations problem of the day janet used a pedometer to count her steps. the...
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10-3 Solving Two-Step Equations
Problem of the Day
Janet used a pedometer to count her steps. The first day and third day she took exactly the same number of steps. The second day she took 1,739 steps. If she took 6,125 steps in all those 3 days, how many steps did she take the first day?
2,193 steps
10-3 Solving Two-Step Equations
Solving Two-Step Equations
10-3 Solving Two-Step Equations
MA.6.A.3.3 Works backward with two-step functions rules to undo expressions.
Also MA.6.A.3.2
Solving Two-Step Equations
10-3 Solving Two-Step Equations
Essential Question:
How are equations applied in the real world?
Solving Two-Step Equations
10-3 Solving Two-Step Equations
Warm Up – Refresh your memory:Solve each equation.
1. 15x = 225
2. y + 2 = 10
Find the value of each expression.
3. 18 – 6 3 5
4. 7 + 3 (16 4) – 2
x = 15
y = 8
8
17
10-3 Solving Two-Step Equations
Solve each equation.
Solving Two-Step Equations
18 + 3x = 30
18 + 3x = 30
– 18 –183x = 12
x = 4
Subtract 18 from both sides to undo the addition.
Divide both sides by 3 to undothe multiplication.
3x3
= 12 3
10-3 Solving Two-Step Equations
Check
18 + 3x = 30
18 + 3(4) 30?=
?=
?=
18 +12 30
30 30
Substitute 4 for x in the equation.
4 is the solution.
10-3 Solving Two-Step Equations
Undo operations in the reverse of the Order of Operations. First undo addition or subtraction. Then undo multiplication or division.
Helpful Hint
10-3 Solving Two-Step Equations
Solving Two-Step Equations
– 2 = 1
– 2 = 1
+ 2 +2
= 3
Add 2 to both sides to undothe subtraction.
Solve. Check the answer.
x = 9
Multiply both sides by 3.
x3
x3
x3
3 · = 3 · 3 x3
10-3 Solving Two-Step Equations
?=
?=
?=
Substitute 9 for x in the equation.
9 is the solution.
Check
– 2 = 1x3
– 2 193
3 – 2 1
1 1
10-3 Solving Two-Step Equations
Solve each equation.
Check It Out: Example 1A
12 + 3x = 27
12 + 3x = 27
– 12 –123x = 15
x = 5
Subtract 12 from both sides to undo the addition.
Divide both sides by 3 to undothe multiplication.
3x3
= 15 3
10-3 Solving Two-Step Equations
Check
Check It Out: Example 1A Continued
12 + 3x = 27
12 + 3(5) 27?=
?=
?=
12 +15 27
27 27
Substitute 5 for x in the equation.
5 is the solution.
10-3 Solving Two-Step Equations
Check It Out: Example 1B
– 1 = 2
– 1 = 2
+ 1 +1
= 3
Add 1 to both sides to undothe subtraction.
Solve. Check the answer.
x = 6
Multiply both sides by 2.
x2
x2
x2
2 · = 2 · 3 x2
10-3 Solving Two-Step Equations
Check It Out: Example 1B Continued
?=
?=
?=
Substitute 6 for x in the equation.
6 is the solution.
Check
– 1 = 2x2
– 1 262
3 – 1 2
2 2
10-3 Solving Two-Step Equations
Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy?
Consumer Math Application
Write a two-step equation to represent the situation.Let x represent the number of CDs Nancy can buy.
cost of a CD timesthe number of CDs
=
The equation 15x + 12 = 87 represents the situation.
cost of headphones
total cost+
15x 12 + 87=
10-3 Solving Two-Step Equations
Solve the equation.
15x + 12 = 87 – 12 –1215x = 75
15x = 7515 15
x = 5
Nancy can buy 5 CDs.
Subtract 12 from both sides.
Divide both sides by 15.
Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy?
10-3 Solving Two-Step Equations
Check It Out: Example 2B
Write a two-step equation to represent the situation.Let d represent the number of days he rented the car.
cost of rental feetimes number of days
=
The equation 20d + 25 = 165 represents the situation.
cost of mileage
total cost+
20d 25 + 165=
Jack rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $165.00. For how many days did he rent the car?
10-3 Solving Two-Step EquationsCheck It Out: Example 2B
Jack rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $165.00. For how many days did he rent the car?
20d + 25 = 165 – 25 – 25
20d = 14020d = 14020 20
d = 7
Jack rented the car for 7 days.
Subtract 25 from both sides.
Divide both sides by 20.
Solve the equation.
10-3 Solving Two-Step Equations
Additional Example 3: Working Backward with Function Rules
The function rule is
5 minus output
The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.
times input 4 equals
5 – yx x 4 =
10-3 Solving Two-Step Equations
Additional Example 3 Continued
5x – 4 = 11
+ 4 + 4
5x = 15
5x = 155 5x = 3
The input value is 3.
Use the function rule and the given output value to write an equation.
Divide both sides by 5.
Add 4 to both sides to undo thesubtraction.
The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.
10-3 Solving Two-Step Equations
Additional Example 3 Continued
Check Substitute the input value into the rule.
5(3) – 4 = 15 – 4 = 11 check
The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.
10-3 Solving Two-Step Equations
Check it Out: Example 3
The function rule is
6 minus output
The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.
times input 3 equals
6 – yx x 3 =
10-3 Solving Two-Step Equations
Check it Out Example 3 Continued
6x – 3 = 9
+ 3 + 3
6x = 12
6x = 126 6x = 2
The input value is 2.
Use the function rule and the given output value to write an equation.
Divide both sides by 6.
Add 3 to both sides to undo thesubtraction.
The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.
10-3 Solving Two-Step Equations
Check it Out Example 3 Continued
Check Substitute the input value into the rule.
6(2) – 3 = 12 – 3 = 9 check
The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.
10-3 Solving Two-Step Equations
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
10-3 Solving Two-Step Equations
Lesson Quiz
Solve each equation. Check your answer.
1. – 7 = 1
2. 22x + 11 = 143
3.
4.
x = 6
x = 96
x = 26
x = 5
x + 95
= 7
9x – 6 = 39
5. In two days, Yasmine drove 505 miles to visit her cousin. The first day, she drove 230 miles. The next day Yasmine drove 5 hours at a constant speed. How fast did Yasmine drive on the second day?
55 mi/h
x12
10-3 Solving Two-Step Equations
1. Solve 4x + 3 = 27.
A. x = 6
B. x = 7.5
B. x = 8
B. x = 96
Lesson Quiz for Student Response Systems
10-3 Solving Two-Step Equations
3. Solve .
A. x = 15
B. x = 20
C. x = 60
D. x = 100
Lesson Quiz for Student Response Systems