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Worksheet: Writing Two-Step Equations

Q1:

Write an equation to describe the following: nine more than the quotient of a number with 6 is 32.

  • A 9 + 6 π‘₯ = 3 2
  • B 9 βˆ’ π‘₯ 6 = 3 2
  • C 9 βˆ’ 6 π‘₯ = 3 2
  • D 9 + π‘₯ 6 = 3 2
  • E 6 + π‘₯ 9 = 3 2

Q2:

Write an equation to describe the following: Negative forty-two is two less than four times a number.

  • A 4 π‘₯ + 2 = 4 2
  • B 4 π‘₯ + 2 = βˆ’ 4 2
  • C 4 π‘₯ βˆ’ 2 = 4 2
  • D 4 π‘₯ βˆ’ 2 = βˆ’ 4 2
  • E 2 π‘₯ + 4 = 4 2

Q3:

Write an equation to find a number, where fifteen less than eight times that number is five times the same number, and then solve it.

  • A 8 π‘₯ + 1 5 = 5 π‘₯ , 5
  • B 1 5 βˆ’ 8 π‘₯ = 5 π‘₯ , 1
  • C 8 π‘₯ βˆ’ 1 5 = 5 , 5
  • D 8 π‘₯ βˆ’ 1 5 = 5 π‘₯ , 5
  • E 5 π‘₯ βˆ’ 1 5 = 8 , 2

Q4:

A cleaning session for a pool in a gym lasts for 35 minutes on weekdays and 45 minutes on weekends. Suppose the time it took to clean the pool last week was 5 hours altogether. Write an equation to represent this information, and then solve it to determine how many weekday cleaning sessions there were.

  • A 3 5 π‘₯ = 3 0 0 , 8 sessions
  • B 4 5 + 3 5 π‘₯ = 3 0 0 , 2 sessions
  • C 4 5 + 4 5 + 3 5 π‘₯ = 3 0 0 , 5 sessions
  • D 4 5 + 4 5 + 3 5 π‘₯ = 3 0 0 , 6 sessions
  • E 4 5 + 3 5 π‘₯ = 3 0 0 , 11 sessions

Q5:

Benjamin wants to join a gym in his neighborhood. It costs $20 for the first subscription plus a monthly fee of $12. If Benjamin has $152 to spend, write and solve an equation to find the number of months he can use the gym.

  • A 2 0 π‘₯ βˆ’ 1 2 = 1 5 2 , 4 months
  • B 1 2 π‘₯ βˆ’ 2 0 = 1 5 2 , 13 months
  • C 1 2 π‘₯ + 2 0 = 1 5 2 , 8 months
  • D 1 2 π‘₯ + 2 0 = 1 5 2 , 11 months
  • E 1 2 π‘₯ βˆ’ 2 0 = 1 5 2 , 14 months

Q6:

A number is tripled and 7 is subtracted from the result. If the answer is 17, what is the number?

Q7:

It took Olivia and Jacob 155 minutes to clean their apartment. Given that Olivia cleaned for 85 minutes longer than Jacob, write an equation to express the amount of time ( π‘š ) that Olivia spent cleaning. Then solve the equation.

  • A π‘š βˆ’ 8 5 = 1 5 5 , π‘š = 2 4 0
  • B π‘š + ( π‘š βˆ’ 8 5 ) = 1 5 5 , π‘š = 3 5
  • C π‘š βˆ’ 8 5 = 1 5 5 , π‘š = 7 0
  • D π‘š + ( π‘š βˆ’ 8 5 ) = 1 5 5 , π‘š = 1 2 0
  • E π‘š + ( π‘š + 8 5 ) = 1 5 5 , π‘š = 3 5

Q8:

The startup cost for a restaurant is $ 1 2 0 0 0 0 , and each meal costs $10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even?

Q9:

Bikes’R’Us is a new company that manufactures bikes. They sell each bike for $250. Given that they had a startup fee of $3 500 and the manufacture cost of each bike is $180, how many bikes do they need to sell to break even?

Q10:

In the given diagram, 𝐴 𝐡 is a straight line. Answer the following questions.

Form an equation that will allow you to calculate π‘₯ .

  • A 6 π‘₯ + 9 8 = 1 8 0
  • B 6 π‘₯ + 1 1 2 = 1 8 0
  • C 6 π‘₯ + 1 4 = 1 1 2
  • D 6 π‘₯ + 1 2 6 = 1 8 0
  • E 6 π‘₯ = 1 1 2

Find the value of π‘₯ .

  • A π‘₯ = 9
  • B π‘₯ = 1 6
  • C π‘₯ = 1 3
  • D π‘₯ = 1 1
  • E π‘₯ = 1 8

Q11:

If π‘š ∠ 1 = 1 1 4 ∘ and π‘š ∠ 2 = ( 2 π‘₯ + 2 1 ) ∘ , find the value of π‘₯ .

Q12:

Given that 𝐷 𝐸 𝐹 𝐺 is a rectangle, π‘š ∠ 𝐸 𝐹 𝐷 = ( 3 π‘₯ + 2 ) ∘ , and π‘š ∠ 𝐷 𝐹 𝐺 = ( 2 π‘₯ + 3 ) ∘ , find π‘š ∠ 𝐸 𝐹 𝐷 .