Solving Equations Packet #2 (Multi-step equations)

Questions 1-16 are from the packet, Questions 17-23 are from the study guide.

Solve for x.


1. 3(2x+10)=54
2. 6(4x+1)=78
3. 2(x+10)=60
4. 4(3x+2)=68

1. 4
2. 3
3. 20
4. 5

Solve for x.


1. 9(2+3x)=45
2. 8(4+x)=64
3. 2(10+10x)=60
4. 4(3+2x)=76

1. 1
2. 4
3. 2
4. 8

Solve for x.


1. 5(2x+10)=50
2. 2(12+3x)=42
3. 15(x+3)=60
4. 2(20+2x)=80

1. 0
2. 3
3. 0
4. 10

Solve for x.


1. 8(2x-10)+4=32
2. 3(4x+3)+4=31
3. 2(x-10)+1=60
4. 4(3x+4)+10=68

1. 6.75
2. 2.75
3. 39.5
4. 3.5

Solve for x.


1. 5(2x-3)-5=45
2. 7(4x-1)-2=47
3. 2(10x-10)-2=60
4. 4(3x-1)-5=75

1. 6.5
2. 2
3. 4.1
4. 7

Solve for x.


1. 5(2x-10)+2=30
2. 2(12x+1)+2=22
3. 15(x+3)+2=60
4. 2(20x-2)-2=36

1. 7.8
2. .75
3. 6 13/15
4. 1.05

Solve for x.


1. 2x+20=12x
2. 6n-12=n+3
3. 12k+15=35+2k

1. 2
2. 3
3. 2

Solve each equation.


1. -3+5a=4a-10
2. -2k=k-7-8
3. -16+3n=-8-5n
4. 4n-1=6n+8-8n+15

1. -7
2. 5
3. 1
4. 4 (*when combining like terms on one side do not do inverse operations*)

Solve each equation.


1. 1-3x=3x+1
2. 4r+8+5=-15-3r
3. -12-4b=4-2b
4. 3n-15=7n+n

1. 0
2. -4
3. -8
4. -3

Solve each equation.


1. -40+2n=4n-8(n+8)
2. 40-x=4(-3-6x)+6
3. 7x-8(-x+7)=-16+7x
4. -8x+32=4(-2-4x)

1. -4
2. -2
3. 5
4. -5

Solve each equation.


1. -7-2x=7(x+8)
2. -6(2r-2)=8r+40
3. 5(-2-3n)=-33+8n
4. -6+3p=8p+2(1-3p)

1. 7
2. -7
3. 1
4. 8

For each rectangle, solve for x and find the length and width.

1. x=3

Length: 9cm, Width: 3cm
2. x=12

Length: 21cm, Width:9

For each shape, solve for x and find the side lengths.

1. x=6

The side length is 13cm
2. x=11

the side length is 31cm
3. x=8

The side length is 15cm.

Leah is running a bake sale for her crew team. She pays $45 for supplies to get started. In addition, it costs about $0.50 to make each item. If baked good items sell for $2 each, determine how many items Leah and her team will need in order to break even.

*Let x=number of items*

Lia’s team needs to sell 30 items to break even.

Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml, and is leaking 10ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?

*Let m=number of minutes*

It will take 50 minutes for the two containers to have the same amount of water.

Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, *m*, will it take for the two containers to have the same amount of water?

*Let m=the amount of minutes*

It will take 25 minutes for both containers to have the same amount of water.

1. What would be the first step in solving for x in the equation?: 2x+8=-10
2. What is the solution of the equation: 15g-63=57
3. What is the solution of the equation: 3n-40+2n=15

1. Subtract 8 from both sides of the equation.
2. g=8
3. n=11

1. What is the solution of the equation: 2(x-2)=6
2. What property do you use when you rewrite the equation 6(x+1)=12 as 6x+6=12
3. Identify the like terms you would combine to solve the equation: -3x+5-2x+8=12
4. What is the solution of the equation: -4(n+5)=-32

1. x=5
2. The distributive property of multiplication over addition
3. -3x and -2x, 5 and 8
4. 3

1. Is x=11 a solution to the given equation? 7x-14-8=9x
2. 8x-27-10-6x=15
3. -3(2x-3)=33

1. No! 55 is not equal to 99- not a solution
2. 26
3. -4

1. The perimeter of the rectangle is 20 units. Write and solve and algebraic equation to find the value of x.
2. The perimeter of the triangle is 30 units. Write and solve and algebraic equation to find the value of x.

1. 2x+12=10 | x=4
2. 14a+2=30 | a=2

1. 6x+22=-3x+31
2. 5x=-7x+6

1. 1
2. 0.5

ONLY WRITE THE ALGEBRAIC EQUATION, DO NOT SOLVE.

UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds, p, will it take for UPS and FedEx to cost the same?

*Let p=number of pounds*

7+.20p=5+.30p

ONLY WRITE THE ALGEBRAIC EQUATION, DO NOT SOLVE.

Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil?

*Let m=number of months*

120+10m=150+4m