2.3 Solve two-step equations You will solve two-step equations Essential question: How do you solve...

2.3 Solve two-step equations

• You will solve two-step equations

• Essential question: How do you solve two-step equations?

Warm-Up ExercisesEXAMPLE 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.

Warm-Up ExercisesEXAMPLE 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

Warm-Up ExercisesGUIDED PRACTICE for Example 1

Solve the equation. Check your solution.1. 5x + 9 = 24

3ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 1

Solve the equation. Check your solution.2. 4y – 4 = 16

5ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 1

Solve the equation. Check your solution.3. –1 = – 7z

3

18ANSWER

Warm-Up ExercisesSolve a two-step equation by combining like termsEXAMPLE 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

Warm-Up ExercisesFind an input of a functionEXAMPLE 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

Warm-Up ExercisesFind an input of a functionEXAMPLE 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

Warm-Up ExercisesFind an input of a functionEXAMPLE 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

Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3

4. 4w + 2w = 24

Solve the equation. Check your solution.

4ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3

5. 8t – 3t = 35

Solve the equation. Check your solution.

7ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3

6. –16 = 5d – 9d

Solve the equation. Check your solution.

4ANSWER

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesGUIDED 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 341

Warm-Up ExercisesEXAMPLE 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.

Warm-Up Exercises

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

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesDaily Homework Quiz

Solve the equation.

1. + 6 = –14 a 4

ANSWER 80–

2. 6r – 12 = 6

ANSWER 3

3. 36 = 7y 2y+–

ANSWER 4–

Warm-Up ExercisesDaily Homework Quiz

The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is –6.

4.

ANSWER y = 3x 9; 1–

A bank charges $5.00 per month plus $.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month.

5.

ANSWER 11 checks

• You will solve two-step equations

• Essential question: How do you solve two-step equations?

First look for like terms and combine them when solving two-step equations. For equations with tow operations, look at the original equation and apply the inverse operations in the reverse order.

• To solve equations efficiently, apply inverse operations in the reverse order of the operations performed on the variable.• Combine like terms before

solving equations.