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Worksheet: Two-Step Equations

Q1:

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

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

Q2:

Solve the equation βˆ’ 6 π‘₯ βˆ’ 1 = βˆ’ 2 3 .

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

Q3:

Given that 8 π‘₯ βˆ’ 9 = 2 3 , find the value of π‘₯ 2 .

Q4:

If π‘₯ Γ— ( 7 βˆ’ ( βˆ’ 4 ) ) = ( βˆ’ 6 Γ— 1 1 ) Γ— 2 , what is the value of π‘₯ ?

Q5:

Solve 1 2 βˆ’ 𝑦 = 3 4 for 𝑦 .

  • A 1 2
  • B 1 4
  • C βˆ’ 3 2
  • D βˆ’ 1 4
  • E 5 4

Q6:

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

  • A 4 3
  • B βˆ’ 1 0 3
  • C16
  • D βˆ’ 4 3
  • E βˆ’ 2

Q7:

Jennifer wants to solve the equation . She wants first to simplify the expression in the brackets, but her friend Victoria says she should expand the expression first. Which way is right?

  • Aneither
  • Bboth but Victoria’s way is shorter
  • Conly Jennifer’s
  • Dboth but Jennifer’s way is shorter
  • Eonly Victoria’s

Q8:

Which of the following equations is equivalent to 2 5 0 0 π‘₯ + 1 2 3 0 = 3 7 0 0 0 0 ?

  • A 2 5 π‘₯ + 1 2 3 = 3 7 0 0 0 0
  • B 2 5 π‘₯ + 1 2 3 = 3 7
  • C 3 7 3 0 π‘₯ = 3 7 0 0 0 0
  • D 2 5 π‘₯ + 1 2 . 3 = 3 7 0 0
  • E 2 5 π‘₯ + 1 . 2 3 = 3 7 0 0

Q9:

What operation was performed on each side of the equation 2 4 . 2 1 5 π‘₯ βˆ’ 7 . 5 2 = 1 4 2 . 8 7 2 to get the equivalent equation 2 4 2 1 5 π‘₯ βˆ’ 7 5 2 0 = 1 4 2 8 7 2 ?

  • Adivision by 1 0 0 0
  • Bmultiplication by 100
  • Cdivision by 100
  • Dmultiplication by 1 0 0 0
  • Emultiplication by 10

Q10:

Determine the solution set of 4 π‘₯ + 6 = βˆ’ 1 4 using the substitution set { βˆ’ 2 0 , βˆ’ 2 , βˆ’ 5 , βˆ’ 8 } .

  • A { βˆ’ 2 }
  • B { βˆ’ 2 0 }
  • C { βˆ’ 8 }
  • D { βˆ’ 5 }

Q11:

Find the solution set of 7 π‘₯ + 1 1 = βˆ’ 2 4 in β„€ .

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

Q12:

Which of the following equations is equivalent to 1 3 π‘₯ + 7 5 = 3 ?

  • A 3 π‘₯ + 7 = 4 5
  • B 5 π‘₯ + 2 1 = 3
  • C 3 π‘₯ + 7 = 3
  • D 5 π‘₯ + 2 1 = 4 5
  • E 5 π‘₯ + 7 = 4 5

Q13:

Solve ( 2 Γ— 2 4 ) + ( 2 Γ— 3 7 ) = 2 Γ— π‘₯ .

Q14:

Find the solution set of the equation 3 π‘₯ βˆ’ 2 0 = | βˆ’ 1 7 | in ℝ .

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

Q15:

The number βˆ’ 6 is a solution to which equation?

  • A βˆ’ 2 π‘₯ + 8 = 1
  • B π‘₯ + 5 = 1
  • C π‘₯ βˆ’ 6 = 2 π‘₯ + 1
  • D βˆ’ 3 π‘₯ + 1 = 1 9

Q16:

Solve 1 2 4 βˆ’ 𝑝 = 9 9 .

  • A 𝑝 = βˆ’ 2 5
  • B 𝑝 = 2 2 3
  • C 𝑝 = 7 1
  • D 𝑝 = 2 5
  • E 𝑝 = 3 4

Q17:

What is the first step in solving the equation 2 π‘₯ + 3 0 = 1 2 ?

  • Adividing each side by 30
  • Badding 30 to each side
  • Cmultiplying each side by 2
  • Dsubtracting 30 from each side
  • Eadding 12 to each side

Q18:

If the solution set of the equation βˆ’ 3 π‘₯ + π‘Ž = βˆ’ 9 is { βˆ’ 2 } , what is the value of π‘Ž ?

  • A 4
  • B βˆ’ 3
  • C βˆ’ 7 3
  • D βˆ’ 1 5

Q19:

If the equation 2 π‘₯ βˆ’ 4 = 2 has the same solution set as the equation π‘Ž π‘₯ + 1 8 = 2 1 , what is the value of π‘Ž ?

Q20:

Solve 9 Γ— 7 2 = 9 Γ— ( π‘₯ + 3 1 ) .

Q21:

Which step should you do first in order to to solve the equation 4 π‘₯ + 8 ο€» 3 + π‘₯ 2  = 1 0 in as few steps as possible?

  • A Take away 10 from both sides.
  • B Take away 4 π‘₯ from both sides.
  • C Divide both sides by 4.
  • D Expand (remove the brackets).
  • E Divide both sides by 8.

Q22:

Find the solution set of 2 π‘₯ + 2 = 4 using the substitution set { 2 , 3 , 1 , 9 } .

  • A { 3 }
  • B { 2 }
  • C { 9 }
  • D { 1 }
  • E { 6 }

Q23:

What is the first step in solving the equation 4 π‘₯ + 4 + 3 π‘₯ + 5 = 1 8 ?

  • Asimplifying 4 π‘₯ + 4 + 3 π‘₯ + 5 into 7 π‘₯ + 5
  • Bsimplifying 4 π‘₯ + 4 + 3 π‘₯ + 5 into 8 π‘₯ + 8
  • Csimplifying 4 π‘₯ + 4 + 3 π‘₯ + 5 into 8 π‘₯ + 9
  • Dsimplifying 4 π‘₯ + 4 + 3 π‘₯ + 5 into 7 π‘₯ + 9
  • Esimplifying 4 π‘₯ + 4 + 3 π‘₯ + 5 into 1 1 π‘₯ + 5

Q24:

Which of the following equations is equivalent to 1 . 5 π‘₯ + 4 . 3 3 = 1 7 . 2 8 ?

  • A 5 . 8 3 π‘₯ = 1 7 . 2 8
  • B 1 5 π‘₯ + 4 3 3 = 1 7 2 8
  • C 1 5 0 π‘₯ + 4 3 3 = 1 7 . 2 8
  • D 1 5 0 π‘₯ + 4 3 3 = 1 7 2 8
  • E 1 5 π‘₯ + 4 3 3 = 1 7 . 2 8

Q25:

Given that ( 𝑛 βˆ’ 5 ) Γ· 4 = 6 , find the value of 𝑛 .