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2-2 Solving Two-Step Equations
Warm UpSolve each equation. 1. 3 + x = 11 2. x – 7 = 19
3. 6x = 15 4.
Find a common denominator.
5.
6.
8 26
12
Possible answer: 6
Possible answer: 20
2-2 Solving Two-Step Equations
Preparation for 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
California Standards
2-2 Solving Two-Step Equations
Additional Example 1A: Solving Two-Step Equations
Solve 18 = 4a + 10.
18 = 4a + 10 First a is multiplied by 4. Then 10 is added.
–10 –10
8 = 4a
2 = a
Subtract 10 from both sides.
8 = 4a is equivalent to 18 = 4a + 10.
Since a is multiplied by 4, divide both sides by 4 to undo the multiplication.
The solution set is {2}.
2-2 Solving Two-Step Equations
Solve the equation. Check your answer.
7.2 = 1.2y
1.5 = 1.2y – 5.7
Check It Out! Example 1b
Add 5.7 to both sides.
7.2 = 1.2y is equivalent to 1.5 = 1.2y – 5.7.
Since y is multiplied by 1.2, divide both sides by 1.2 to undo the multiplication.
The solution set is {6}.
First y is multiplied by 1.2. Then 5.7 is subtracted.
+ 5.7 +5.7
6 = y
1.5 = 1.2y – 5.7
2-2 Solving Two-Step Equations
Solve the equation. Check your answer.
Check It Out! Example 1c
n = 0
Subtract 2 from each side.
Since n is divided by 7, multiply both sides by 7 to undo the division.
The solution set is {0}.
First n is divided by 7. Then 2 is added.
–2 –2
= 0 = 0 is equivalent to + 2 = 2.
2-2 Solving Two-Step Equations
Additional Example 2A: Solving Two-Step Equations That Contain Fractions
Solve the equation.
Method 1 Use fraction operations.
Since is subtracted from , add to
both sides to undo the subtraction.
2-2 Solving Two-Step Equations
Additional Example 2A Continued
y = 16
Since y is divided by 8 multiply both sides by 8.
Simplify.
The solution set is {16}.
2-2 Solving Two-Step Equations
Check It Out! Example 2c
Solve the equation. Check your answer.
Method 1 Use fraction operations.
Since is subtracted from , add
to both sides to undo the subtraction.
2-2 Solving Two-Step Equations
Check It Out! Example 2c Continued
Simplify.
The solution set is {15}.n = 15
Since n is multiplied by multiply both
sides by the reciprocal, .
2-2 Solving Two-Step Equations
Check It Out! Example 2c Continued
Check
To check your solution, substitute 15 for n in the original equation.
2-2 Solving Two-Step Equations
Check It Out! Example 3b
Lynda has 12 CDs in her collection. She adds the same number of new CDs to her collection each month. After 7 months Lynda has 26 CDs. How many records does Lynda add each month?
The answer will be the number of records that Lynda adds each month.
• Lynda started with 12 records.
• Lynda adds records each month.
• At the end of 7 months she had 26 records.
Let r represent the number of records added monthly.
2-2 Solving Two-Step Equations
Months is total records
Solve33
7r + 12 = 26–12 –12
7r = 14
r = 2 records a month
Since 12 is added to 7r, subtract 12 from both sides to undo the addition.
Since r is multiplied by 7, divide both sides by 7 to undo the multiplication.
initial records
plus
7r = 2612+
Check It Out! Example 3b Continued
2-2 Solving Two-Step Equations
Look Back44
Check that the answer is reasonable. The number of records added per month is 2, so if Lynda started with 12 records and added the 2 per month for 7 months, the total number is equal to 26.
Check It Out! Example 3b Continued
2-2 Solving Two-Step EquationsLesson Quiz
Solve each equation.
1. 4y + 8 = 2 2. 3 + 2x = 11
3. 4.
4
–8
5. Nancy bought 5 rolls of color film and 6 rolls of black-and-white film. The 5 rolls of color film cost $15, and Nancy’s total was $39. Write and solve an equation to find the cost of one roll of black-and-white film.
6b + 15 = 39; $4