ALGEBRA

Solving Multistep Equations

Objective

• Write and solve multistep equations.

ALGEBRA

Solving Multistep Equations

The goal is to get the variable on one side of the equal sign and the numbers on the other side.

Key Skills

Keep it balanced!Solve 6n + 17 = 5 + 4n

– 6n – 6n

17 = 5 – 2n

–5 –5

12 = – 2n

Where do we start?Does it matter?Like driving to Seaside Heights, you could take the Turnpike to the Parkway or Route 280 to the Parkway. Either way gets you to the Parkway which you need to take to get to Seaside Heights.÷ – 2 ÷ – 2

Subtract 6n from each side of the equal sign.

Subtract 5 from each side of the equal sign.

Divide by – 2

n = – 6

ALGEBRA

Solving Multistep Equations

Key Skills

Keep it balanced!Solve 3x + 19 = 4 + 8x

x = 3

The goal is to get the variable on one side of the equal sign and the numbers on the other side.

Subtract 3x from each side of the equal sign.

– 3x – 3x

19 = 4 + 5x Subtract 4 from each side of the equal sign.

–4 –4

15 = 5xDivide by 5

÷ 5 ÷ 5

ALGEBRA

Solving Multistep Equations

Try This

Keep it balanced!Solve – 3x – 9 = – 13 – 7x

x = – 1

The goal is to get the variable on one side of the equal sign and the numbers on the other side.

Add 3x to each side of the equal sign.

+ 3x + 3x

– 9 = – 13 – 4x Add 13 to each side of the equal sign.

+13 +13

4 = – 4xDivide by – 4

÷ – 4 ÷ – 4

ALGEBRA

Solving Multistep Equations

ALGEBRA

Solving Multistep Equations

Do this togetherMr. Esker has to buy pencils for his company. Supplier A charges $4 per box and $3 for shipping. Supplier B charges $3 per box and $6 for shipping.

a. Write equations for both suppliers.

b. How many boxes would he need to buy for both companies to charge the same amount?

ALGEBRA

Solving Multistep Equations

Do this togetherMr. Esker has to buy pencils for his company. Supplier A charges $4 per box and $3 for shipping. Supplier B charges $3 per box and $6 for shipping.

To write the equation for Supplier A, the Cost (what you end up paying) is equal to

C =

the shipping cost (fixed amount, the constant where the cost starts)

$3

+ the cost per box multiplied by how boxes are purchased.

+ 4b

Try writing the equation for Supplier B. C = $6 + 3b

ALGEBRA

Solving Multistep Equations

Do this togetherIn order to find when the 2 Suppliers charge the same amount, set the 2 equations equal to each other.

C = 4b + 3 C = 3b + 6

4b + 3 = 3b + 6

Now Solve for b.

ALGEBRA

Solving Multistep Equations

Do this together

Solve 4b + 3 = 3b + 6

3 = b

The goal is to get the variable on one side of the equal sign and the numbers on the other side.

Subtract 4b from each side of the equal sign.

– 4b – 4b

3 = – b + 6 Subtract 6 from each side of the equal sign.

– 6 – 6

– 3 = – bDivide by – 1

÷ – 1 ÷ – 1

ALGEBRA

Solving Multistep Equations

Try ThisA car leaves Newark airport and travels at a constant rate of 65 mph to Los Angeles. The car travels through Pittsburgh, which is 370 miles from Newark, and through Las Vegas, which is 2500 miles from Newark.

When the car gets to Las Vegas, an airplane leaves Pittsburgh and travels at a constant rate of 550 mph to LA. It travels over Las Vegas as well. When will the airplane fly over the car?

ALGEBRA

Solving Multistep Equations

Try ThisLet d equal the distance traveled and h equal the elapsed time, the distances must be equal. The important facts are the speeds and how far each vehicle is from Newark when the plane takes off.

d = 550h + 370Car

Airplaned = 65h + 2500

550h + 370 = 65h + 2500

ALGEBRA

Solving Multistep Equations

Try This

550h + 370 = 65h + 2500

– 65h – 65h

485h = 2130

÷ 485 ÷ 485

h = 4.4 hours or 4 hours 24 minutes

– 370 – 370

550h = 65h + 2130