3.2 Solve Two-Step Equations

• Students will solve two-step equations using Algebra.

• Students will do assigned homework.

• Students will studyvocabulary words.

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Lesson 3.2, For use with pages 141-146

Solve the equation.

1. 3x = –18

ANSWER –6

ANSWER –10

2. b + 21 = 11

Lesson 3.2, For use with pages 141-146

Solve the equation.

3. Simplify the expression 3(x + 2) – 4x + 1.

ANSWER –x + 7

4. There are three times as many goats as sheep in a petting zoo. Find the number of sheep if the totalnumber of goats and sheep is 28.

ANSWER 7 sheep

Daily Homework Quiz For use after Lesson 3.1

2. 8 = m – 7

ANSWER 15

ANSWER 4

3. 9k = –72

ANSWER –8

1. –6 + a = –2

Solve the equation. Check your solution.

Daily Homework Quiz For use after Lesson 3.1

ANSWER –60

ANSWER 16.78 sec

4. 12 = x–5

5. Earth orbits the Sun at an average speed of 29.79 kilometers per second. Find how long it takes, to the nearest hundredth of a second, for Earth to travel 500 kilometers.

EXAMPLE 1 Solve a two-step equation

Solve + 5 = 11.x2

Write original equation.+ 5 = x2 11

+ 5 – 5 = x2 11 – 5 Subtract 5 from each side.

= x2 6 Simplify.

2 =x2 2 6 Multiply each side by 2.

x =12 Simplify.

ANSWER

The solution is 12. Check by substituting 12 for x in the original equation.

EXAMPLE 1 Solve a two-step equation

CHECK + 5 = x2 11 Write original equation.

11+ 5 = 122

?Substitute 12 for x.

Simplify. Solution checks.11 =11

GUIDED PRACTICE for Example 1

Solve the equation. Check your solution.

1. 5x + 9 = 24

3ANSWER

GUIDED PRACTICE for Example 1

Solve the equation. Check your solution.

2. 4y – 4 = 16

5ANSWER

GUIDED PRACTICE for Example 1

Solve the equation. Check your solution.

3. –1 = – 7z3

18ANSWER

Solve a two-step equation by combining like terms

EXAMPLE 2

Solve 7x – 4x = 21

7x – 4x = 21

Write original equation.

3x = 21

Combine like terms.

Divide each side by 3.

x = 7 Simplify.

=33x

321

Find an input of a function

EXAMPLE 3

The output of a function is 3 less than 5 times the input. Find the input when the output is 17.

y = 5x – 3

y is 3 less than 5 times x.

SOLUTION

Write an equation for the function. Let x be the input and y be the output

STEP 1

Solve the equation for x when y = 17.

STEP 2

Find an input of a function

EXAMPLE 3

y = 5x – 3

Write original function.

17 = 5x – 3

Substitute 17 for y.

17 + 3 = 5x – 3 + 3

Add 3 to each side.

20 = 5x

Simplify.

Divide each side by 5.

4 = x Simplify.

ANSWER

An input of 4 produces an output of 17.

=520 5x

5

Find an input of a function

EXAMPLE 3

Write original function.

Substitute 17 for y and 4 for x.

Multiply 5 and 4.

Simplify. Solution checks.

CHECK

17 = 20 – 3

?

17 = 5(4) – 3

?

17 = 17

y = 5x – 3

GUIDED PRACTICE for Examples 2 and 3

4. 4w + 2w = 24

Solve the equation. Check your solution.

4ANSWER

GUIDED PRACTICE for Examples 2 and 3

5. 8t – 3t = 35

Solve the equation. Check your solution.

7ANSWER

GUIDED PRACTICE for Examples 2 and 3

6. –16 = 5d – 9d

Solve the equation. Check your solution.

4ANSWER

GUIDED PRACTICE for Examples 2 and 3

7. The output of a function is 5 more than –2 times the input. Find the input when the output is 11.

ANSWER –3

GUIDED PRACTICE for Examples 2 And 3

8. The output of a function is 4 less than 4 times the input. Find the input when the output is 3

ANSWER 34

1

EXAMPLE 4 Solve a multi-step problem

As a scuba diver descends into deeper water, the pressure of the water on the diver’s body steadily increases.

SCUBA DIVING

The pressure at the surface of the water is 2117 pounds per square foot (lb/ft2). The pressure increases at a rate of 64 pounds per square foot for each foot the diver descends. Find the depth at which a diver experiences a pressure of 8517 pounds per square foot.

SOLUTION

EXAMPLE 1

Write a verbal model. Then write an equation.

Find the depth at which the pressure is 8517 pounds per square foot.

P = 2117 + 64d

Write equation.

STEP 1

STEP 2

EXAMPLE 4 Solve a multi-step problem

GUIDED PRACTICE

Substitute 8517 for P.

8517 – 2117 = 2117 – 2117 + 64d

Subtract 2117 from each side.

8517 = 2117 + 64d

6400 = 64d

Simplify.

Divide each side by 64.

100 = d Simplify.

ANSWER

A diver experiences a pressure of 8517 pounds per square foot at a depth of 100 feet.

64640064 = 64d

EXAMPLE 4 Solve a multi-step problem

GUIDED PRACTICE

P = 2117 + 64d

Write original equation.

Substitute 8517 for P and 100 for d.

Multiply 64 and 100.

Simplify. Solution checks.

8517 2117 + 6400?=

8517 2117 + 64(100)?=

CHECK

EXAMPLE 4 Solve a multi-step problem

8517 = 8517

GUIDED PRACTICE for Example 4

WHAT IF? In Example 4, suppose the diver experiences a pressure of 5317 pounds per square foot. Find the diver’s depth.

9.

ANSWER 50 ft

GUIDED PRACTICE for Example 4

Jobs

Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work?

10.

5 hANSWER

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