Warm-Up Exercises
Solve the equation.
1. 2m – 6 + 4m = 12
ANSWER
3
2. 6a – 5(a – 1) = 11
ANSWER
6
Warm-Up Exercises
Solve the equation.
3. A charter bus company charges $11.25 per ticket
plus a handling charge of $.50 per ticket, and a $15
fee for booking the bus. If a group pays $297 to
charter a bus, how many tickets did they buy?
ANSWER
24 tickets
Warm-Up1Exercises
EXAMPLE
Solve an equation with variables on both sides
Solve 7 – 8x = 4x – 17.
7 – 8x = 4x – 17
7 – 8x + 8x = 4x – 17 + 8x
7 = 12x – 17
24 = 12x
2=x
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.
Warm-Up1Exercises
EXAMPLE
Solve an equation with variables on both sides
CHECK
7 – 8x = 4x – 17
?
7 – 8(2) = 4(2) – 17
?
Write original equation.
Substitute 2 for x.
–9 = 4(2) – 17
Simplify left side.
–9 = –9
Simplify right side. Solution checks.
Warm-Up2Exercises
EXAMPLE
Solve an equation with grouping symbols
1
Solve 9x – 5 = 4 (16x + 60).
1
9x – 5 = (16x + 60)
4
Write original equation.
9x – 5 = 4x + 15
Distributive property
5x – 5 = 15
Subtract 4x from each side.
5x = 20
x=4
Add 5 to each side.
Divide each side by 5.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
2. 20 + c = 4c – 7
ANSWER
9
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
3. 9 – 3k = 17k – 2k
ANSWER
–8
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
4. 5z – 2 = 5+3(3z – 4)
ANSWER
5
12
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
5. 3 – 4a = 5(a – 3)
ANSWER
2
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4
Solve the equation, if possible.
8.
9z + 12 = 9(z + 3)
ANSWER
no solution
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4
Solve the equation, if possible.
9. 7w + 1 = 8w + 1
ANSWER
0
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4
Solve the equation, if possible.
10. 3(2a + 2) = 2(3a + 3)
ANSWER
identity
Daily
Homework
Quiz
Warm-Up
Exercises
Solve the equation, if possible.
1.
3(3x + 6) = 9(x + 2)
ANSWER
2.
7(h – 4) = 2h + 17
ANSWER
3.
The equation is an identity.
9
8 – 2w = 6w – 8
ANSWER
2
Daily
Homework
Quiz
Warm-Up
Exercises
4.
4g + 3 = 2(2g + 3)
ANSWER
5.
The equation has no solution.
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?
ANSWER
5h