warm-up exercises 1. 2m – 6 + 4m = 12 answer 6 solve the equation. 2.6a – 5(a – 1) = 11 answer...
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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.