Writing Two Step Equations

Writing Two Step Equations

Two Step Equations have two operations, a variable with a coefficient or divisor, a constant, and an equal sign.

• 2x + 8 = 19

•  $3-\frac{x}{5}=\ -12$  

This is an example of how to solve a 2 step. The 3 is the divisor in this two step

Multiple Select

Choose all of the equations that are two step equations.

• $\frac{x}{5\ }=\ 4$

• $6=\ 7\ -\ \frac{x}{3}$

• $12x\ -14=\ -2$

• $\frac{x}{6}\ +\ 7$

Write a two step:

Valery had $15. She wanted to purchase some headphones that were $75. If she saves $3 a week from her chores, how long will it take her to reach her goal?

• 15 + 3w = 75

• w= 20

David had $255. If he goes below the balance of 25 then he gets charged each day it is below. He spends $10 a day on lunch. How many days until can he do this before he gets charged?

• 255- 10x = 25

• x = 23

Write a two step:
Lesly and her 2 friends did some lawn work for a neighbor. Lesly split the amount they were paid equally among them. Lesly  stayed and did some work by herself and earned another $10. She now has $28. How much did the neighbor pay them to do the lawn work?

•  $\frac{x}{3}\ +\ 10\ =\ 28$  
  

• x =54

Mark's goal was to save $150. He owes his mom $30 and he makes $10 per hour tending to the bulls. How many hours will he need to work to reach his goal?

• -30 + 10x = 150

• x = 18

Reminder! Watch out for negatives!

• debt, withdrawal, take away

Multiple Choice

Bonnie spent half of her weekly allowance playing mini-golf. To earn more money her parents let her wash the car for $4. What is her weekly allowance if she ended with $12?  (Define 'n' and write the equation.) 

• n=wkly allowance; 2n-4=12
• n=wkly allowance; 2n+4=12
• n=wkly allowance; n/2-4=12
• n=wkly allowance; n/2+4=12

Multiple Choice

WRITE AN EQUATION
April had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

• n=total cost pencils; 7n+10=24
• n=cost of 1 pencil; 7n-10=24
• n=cost of 1 pencil; 7n+10=24
• n=cost of 1 pencil; -7n-10=24

Multiple Choice

Which equation matches the following situation? 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

• n= # of students in each bus; 6n + 7 =331
• n=# of buses; 6n + 7 =331
• n= # of students in each bus; 6 + 7n =331
• n= # of students in each bus; 6n - 7 =331

Multiple Choice

A cell phone company charges $3.00 to make a phone call plus $0.15 for each minute for each minute you talk. Which equation would you use to determine the total cost, c, of a phone call that is m number of minutes long?

• c = 3.00 - 0.15m
• c = 0.15 + 3.00m
• 3.00 = c + 0.15
• c = 3.00 + 0.15m

Multiple Choice

Casey has $50 to spend at Best Buy. She wants to buy a DVD for $14 and some CDs that cost $12 each. How many CDs can she buy?

• 12 + 14x = 50

• 12x + 14 = 50

• 50 - 14 - 12 = x

• 50x + 12 = 14

Multiple Choice

Write an equation for the following:

Twice a number plus 6 is -72

• 2 + 6x =- 72

• 2x + 6 = -72

• 2 + 6 = x

• 2x² + 6 = 72

Multiple Choice

A banana has 85 calories. This is 10 calories less than one eighth of the calories in a banana split. Which equations helps you find how many calories are in a banana split?

• 85 - 10 = x
• x/8 + 10 = 85
• x/8 - 10 = 85
• x/8 - 10 = 75

Multiple Choice

Ken is thinking of a number. Nine more than the product of 4 and the number is 73. What is the equation?

• 4 + 9x = 73
• 4x = 73
• 4x + 9 = 73
• 9x + 4 = 73

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation to find out how many hours, h, they rented the Boat if the total cost was $33.

• h = 2(9) + 15
• 33 = 15h + 2
• h = 15(9) + 2
• 33 = 2h + 15

Multiple Choice

Figure out the solution to this equation: -4x + 1 = 21

• x = 120
• x = 5
• x = 30
• x = -5