Worksheet: Two-Step Equations

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

Q1:

Find the solution set of 3 𝑥 − 9 = − 6 in ℕ .

  • A { 6 }
  • B { 3 }
  • C ∅
  • D { 1 }

Q2:

Solve the equation − 6 𝑥 − 1 = − 2 3 .

  • A 𝑥 = 1 7
  • B 𝑥 = 4
  • C 𝑥 = − 1 6
  • D 𝑥 = 1 1 3

Q3:

Given that 8 𝑥 − 9 = 2 3 , find the value of 𝑥 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 𝑥 for which 5 𝑥 + 4 = − 5 .

  • A 𝑥 = − 4 5
  • B 𝑥 = − 1 5
  • C 𝑥 = − 5
  • D 𝑥 = − 9 5
  • E 𝑥 = − 9

Q6:

It took Dalia and Bassem 155 minutes to clean their flat. Given that Dalia cleaned for 85 minutes longer than Bassem, write an equation to express the amount of time ( 𝑚 ) that Dalia spent cleaning. Then solve the equation.

  • A 𝑚 − 8 5 = 1 5 5 , 𝑚 = 2 4 0
  • B 𝑚 + ( 𝑚 − 8 5 ) = 1 5 5 , 𝑚 = 3 5
  • C 𝑚 − 8 5 = 1 5 5 , 𝑚 = 7 0
  • D 𝑚 + ( 𝑚 − 8 5 ) = 1 5 5 , 𝑚 = 1 2 0
  • E 𝑚 + ( 𝑚 + 8 5 ) = 1 5 5 , 𝑚 = 3 5

Q7:

Find the solution set of the equation 3 𝑥 − 2 0 = | − 1 7 | in ℝ .

  • A { 1 }
  • B { − 1 }
  • C − 3 7 3
  • D 3 7 3
  • E { 3 7 }

Q8:

If 4 7 − 2 𝑥 = 2 7 , what is the value of 𝑥 ?

Q9:

Find the solution set of the equation − 4 𝑥 + 3 = 4 .

  • A { − 3 }
  • B − 7 4
  • C { 1 }
  • D − 1 4

Q10:

Which of the following equations has a solution set of { − 2 } ?

  • A 3 𝑧 − 1 4 = 8
  • B 3 𝑧 = 2 5
  • C 4 𝑧 + 9 = 1 9
  • D 3 𝑧 + 1 4 = 8

Q11:

Which of the following equations is equivalent to 3 𝑦 − 1 = 5 ?

  • A 4 𝑦 − 1 4 = 2 2
  • B 4 𝑦 = 4 0
  • C 3 𝑦 + 1 = 5
  • D 4 𝑦 + 1 4 = 2 2

Q12:

Answer the following questions using the given diagram.

Form an equation that will allow you to calculate 𝑥 .

  • A 7 𝑥 + 3 = 1 8 0
  • B 7 𝑥 + 3 = 1 1 4
  • C 7 𝑥 + 3 = 3 3
  • D 7 𝑥 + 3 = 6 6
  • E 7 𝑥 + 3 = 9 0

Find the value of 𝑥 .

  • A 𝑥 = 9
  • B 𝑥 = 5
  • C 𝑥 = 2 5
  • D 𝑥 = 1 6
  • E 𝑥 = 1 3

Q13:

Find the solution set of 𝑥 4 − 3 = − 5 in ℤ .

  • A { 3 2 }
  • B { − 2 }
  • C { 8 }
  • D { − 8 }

Q14:

Solve 8 𝑘 − 3 − 2 𝑘 = 2 1 .

Q15:

Bassem 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 8 𝑥 + 3 = 5 1 , where 𝑥 is the number of stamps.

Q16:

Fady 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 he has by solving for .

Q17:

Solve 7 ( 𝑦 − 2 ) = − 2 8 .

Q18:

Find the solution set of 8 𝑥 − 8 = 1 6 in ℤ .

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

Q19:

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

  • A 9 + 6 𝑥 = 3 2
  • B 9 − 𝑥 6 = 3 2
  • C 9 − 6 𝑥 = 3 2
  • D 9 + 𝑥 6 = 3 2
  • E 6 + 𝑥 9 = 3 2

Q20:

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

Form an equation that will allow you to calculate 𝑥 .

  • A 6 𝑥 + 9 8 = 1 8 0
  • B 6 𝑥 + 1 1 2 = 1 8 0
  • C 6 𝑥 + 1 4 = 1 1 2
  • D 6 𝑥 + 1 2 6 = 1 8 0
  • E 6 𝑥 = 1 1 2

Find the value of 𝑥 .

  • A 𝑥 = 9
  • B 𝑥 = 1 6
  • C 𝑥 = 1 3
  • D 𝑥 = 1 1
  • E 𝑥 = 1 8

Q21:

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

  • A 8 𝑥 + 5 0 = 3 𝑥 , 10
  • B 5 0 − 8 𝑥 = 3 𝑥 , 4
  • C 8 𝑥 − 5 0 = 3 , 3
  • D 8 𝑥 − 5 0 = 3 𝑥 , 10
  • E 3 𝑥 − 5 0 = 8 , 6

Q22:

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 𝑥 = 3 0 0 , 8 sessions
  • B 4 5 + 3 5 𝑥 = 3 0 0 , 2 sessions
  • C 4 5 + 4 5 + 3 5 𝑥 = 3 0 0 , 5 sessions
  • D 4 5 + 4 5 + 3 5 𝑥 = 3 0 0 , 6 sessions
  • E 4 5 + 3 5 𝑥 = 3 0 0 , 11 sessions

Q23:

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

Q24:

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

  • A , 4 months
  • B , 13 months
  • C , 8 months
  • D , 11 months
  • E , 14 months

Q25:

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

  • A 4 𝑥 + 2 = 4 2
  • B 4 𝑥 + 2 = − 4 2
  • C 4 𝑥 − 2 = 4 2
  • D 4 𝑥 − 2 = − 4 2
  • E 2 𝑥 + 4 = 4 2

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