Warm-Up Exercises

1. 2m – 6 + 4m = 12

ANSWER 6

Solve the equation.

2. 6a – 5(a – 1) = 11

ANSWER 3

Warm-Up Exercises

3. A charter bus company charges $11.25 per ticketplus a handling charge of $.50 per ticket, and a $15fee for booking the bus. If a group pays $297 to charter a bus, how many tickets did they buy?

ANSWER 24 tickets

Solve the equation.

Warm-Up ExercisesEXAMPLE 1 Solve an equation with variables on both sides

7 – 8x = 4x – 17

7 – 8x + 8x = 4x – 17 + 8x

7 = 12x – 17

24 = 12x

Write original equation.

Add 8x to each side.

Simplify each side.

Add 17 to each side.

Divide each side by 12.

ANSWER

The solution is 2. Check by substituting 2 for x in the original equation.

Solve 7 – 8x = 4x – 17.

2 = x

Warm-Up ExercisesEXAMPLE 1 Solve an equation with variables on both sides

Write original equation.

Substitute 2 for x.

Simplify left side.

Simplify right side. Solution checks.

–9 = 4(2) – 17?

7 – 8(2) = 4(2) – 17?

7 – 8x = 4x – 17 CHECK

–9 = –9

Warm-Up ExercisesEXAMPLE 2 Solve an equation with grouping symbols

14

(16x + 60)9x – 5 =

9x – 5 = 4x + 15

5x – 5 = 15

5x = 20

x = 4

Write original equation.

Distributive property

Subtract 4x from each side.

Add 5 to each side.

Divide each side by 5.

9x – 5 =14 (16x + 60).Solve

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

2. 20 + c = 4c – 7

ANSWER 9

Solve the equation. Check your solution.

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

3. 9 – 3k = 17k – 2k

Solve the equation. Check your solution.

ANSWER –8

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

4. 5z – 2 = 5+3(3z – 4)

Solve the equation. Check your solution.

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

5. 3 – 4a = 5(a – 3)

Solve the equation. Check your solution.

ANSWER 2

Warm-Up ExercisesGUIDED PRACTICE for Example 4

8. 9z + 12 = 9(z + 3)

Solve the equation, if possible.

ANSWER

no solution

Warm-Up ExercisesGUIDED PRACTICE for Example 4

9. 7w + 1 = 8w + 1

ANSWER

0

Solve the equation, if possible.

Warm-Up ExercisesGUIDED PRACTICE for Example 4

10. 3(2a + 2) = 2(3a + 3)

ANSWER

identity

Solve the equation, if possible.

Warm-Up ExercisesDaily Homework Quiz

Solve the equation, if possible.

3(3x + 6) = 9(x + 2)1.

7(h – 4) = 2h + 172.

ANSWER The equation is an identity.

ANSWER 9

8 – 2w = 6w – 83.

ANSWER 2

Warm-Up ExercisesDaily Homework Quiz

4g + 3 = 2(2g + 3)4.

ANSWER The equation has no solution.

ANSWER 5 h

Bryson is looking for a repair service for general household maintenance. One service charges $75 to join the service and $30 per hour. Another service charge $45 per hour. After how many hours of service is the total cost for the two services the same?

5.