Worksheet: Two-Step Equations

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In this worksheet, we will practice solving two-step equations.

Q1:

Find the solution set of 3π‘₯βˆ’9=βˆ’6 in β„•.

  • A { 3 }
  • B { 6 }
  • C { 1 }
  • D βˆ…

Q2:

Solve the equation βˆ’6π‘₯βˆ’1=βˆ’23.

  • A π‘₯ = 1 7
  • B π‘₯ = 4
  • C π‘₯ = βˆ’ 1 6
  • D π‘₯ = 1 1 3

Q3:

Given that 8π‘₯βˆ’9=23, find the value of π‘₯2.

Q4:

I think of a number, multiply it by 2 and subtract 1 from the answer. The result is 9. What is my number?

Q5:

Find the value of π‘₯ for which 5π‘₯+4=βˆ’5.

  • A π‘₯ = βˆ’ 1 5
  • B π‘₯ = βˆ’ 4 5
  • C π‘₯ = βˆ’ 9 5
  • D π‘₯ = βˆ’ 9
  • E π‘₯ = βˆ’ 5

Q6:

Find the solution set of the equation 3π‘₯βˆ’20=|βˆ’17| in ℝ.

  • A  βˆ’ 3 7 3 
  • B  3 7 3 
  • C { 3 7 }
  • D { βˆ’ 1 }
  • E { 1 }

Q7:

If 47βˆ’2π‘₯=27, what is the value of π‘₯?

Q8:

Find the solution set of the equation βˆ’4π‘₯+3=4.

  • A { 1 }
  • B  βˆ’ 7 4 
  • C  βˆ’ 1 4 
  • D { βˆ’ 3 }

Q9:

Answer the following questions using the given diagram.

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

  • A 7 π‘₯ + 3 = 9 0
  • B 7 π‘₯ + 3 = 1 8 0
  • C 7 π‘₯ + 3 = 6 6
  • D 7 π‘₯ + 3 = 3 3
  • E 7 π‘₯ + 3 = 1 1 4

Find the value of π‘₯.

  • A π‘₯ = 2 5
  • B π‘₯ = 1 6
  • C π‘₯ = 9
  • D π‘₯ = 5
  • E π‘₯ = 1 3

Q10:

Find the solution set of π‘₯4βˆ’3=βˆ’5 in β„€.

  • A { 8 }
  • B { βˆ’ 2 }
  • C { 3 2 }
  • D { βˆ’ 8 }

Q11:

Jacob has a collection of 51 stamps. When he was moving, he put the same number of stamps in each of the first 8 albums and 3 stamps in the last album. Find the number of stamps in each of the first eight folders by solving the equation 8π‘₯+3=51, where π‘₯ is the number of stamps.

Q12:

Michael has 34 marbles. He has the same number of red, yellow, and blue marbles, as well as 7 multicolored marbles. Determine the number of yellow marbles π‘₯ he has by solving 3π‘₯+7=34 for π‘₯.

Q13:

Solve 7(π‘¦βˆ’2)=βˆ’28.

Q14:

Find the solution set of 8π‘₯βˆ’8=16 in β„€.

  • A { 1 }
  • B { 2 4 }
  • C { 3 }
  • D { 8 }

Q15:

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

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

Q16:

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

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

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

Find the value of π‘₯.

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

Q17:

The pool of a gym is regularly cleaned. A cleaning session lasts for 35 minutes on weekdays and 45 minutes on weekends. The time it took to clean the pool last week was 5 hours altogether. Given that it was cleaned twice on the weekend, write an equation to represent this information, and then solve it to determine how many weekday cleaning sessions there were.

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

Q18:

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

Q19:

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

Q20:

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

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

Q21:

Find the solution set of 7π‘₯+11=βˆ’24 in β„€.

  • A { 1 3 }
  • B { 1 }
  • C { βˆ’ 3 5 }
  • D { βˆ’ 5 }

Q22:

If π‘₯Γ—(7βˆ’(βˆ’4))=(βˆ’6Γ—11)Γ—2, what is the value of π‘₯?

Q23:

Given π‘¦βˆ’3π‘₯=7, calculate the value of π‘₯ when 𝑦=3.

  • A 4 3
  • B16
  • C βˆ’ 2
  • D βˆ’ 1 0 3
  • E βˆ’ 4 3

Q24:

Grace wants to solve the equation 𝑣(14βˆ’8)=21. She wants first to simplify the expression in the brackets, but her friend Megan says she should expand the expression first. Which way is right?

  • Aboth but Grace’s way is shorter
  • Bneither
  • Conly Grace’s
  • Dboth but Megan’s way is shorter
  • Eonly Megan’s

Q25:

Solve (2Γ—24)+(2Γ—37)=2Γ—π‘₯.

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