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Worksheet: One-Step Equations

Q1:

Solve π‘₯ βˆ’ 6 7 = 8 1 .

Q2:

Determine whether the following statement is sometimes, always, or never true: Equations like π‘Ž + 1 0 = 1 1 and 1 6 βˆ’ π‘š = 3 have only one solution.

  • Anever
  • Bsometimes
  • Calways

Q3:

What is the first step in solving the equation βˆ’ 2 1 𝑦 = 8 . 4 ?

  • Asubtracting βˆ’ 2 1 from each side
  • Bmultiplying each side by βˆ’ 2 1
  • Cadding βˆ’ 2 1 to each side
  • Ddividing each side by βˆ’ 2 1
  • Edividing each side by 8.4

Q4:

Solve 𝑦 1 1 = βˆ’ 1 1 .

Q5:

What is the first step in solving the equation 𝑑 Γ· ( βˆ’ 3 ) = 4 6 7 ?

  • Asubtracting βˆ’ 3 from each side
  • Bdividing each side by βˆ’ 3
  • Cadding βˆ’ 3 to each side
  • Dmultiplying each side by βˆ’ 3
  • Edividing each side by 3

Q6:

Suppose π‘š ∠ 𝐷 = ( π‘₯ βˆ’ 2 ) ∘ . Find π‘₯ so that ∠ 𝐷 is a right angle.

Q7:

What is the first step in solving the equation 4 π‘₯ = βˆ’ 1 2 4 ?

  • Asubtracting 4 from each side
  • Bmultiplying each side by 4
  • Cadding 4 to each side
  • Ddividing each side by 4
  • Edividing each side by βˆ’ 1 2 4

Q8:

Find the solution set of π‘₯ + 6 = 1 in β„• .

  • A { 7 }
  • B { βˆ’ 5 }
  • C { βˆ’ 7 }
  • D βˆ…

Q9:

Solve 1 3 = π‘₯ + 5 .

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

Q10:

What is the first step in solving the equation 3 𝑔 = 1 1 0 ?

  • Asubtracting 3 from each side
  • Bmultiplying each side by 3
  • Cadding 3 to each side
  • Ddividing each side by 3
  • Edividing each side by 110

Q11:

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

  • A  1 3 
  • B βˆ…
  • C { 4 8 }
  • D { 3 }

Q12:

Solve 3 π‘₯ = 3 0 .

  • A π‘₯ = 2 7
  • B π‘₯ = 9 0
  • C π‘₯ = 3 3
  • D π‘₯ = 1 0
  • E π‘₯ = βˆ’ 1 0

Q13:

Solve 4 π‘₯ = 3 for π‘₯ .

  • A βˆ’ 1
  • B 4 3
  • C1
  • D 3 4
  • E12

Q14:

Find the value of 𝑏 given 7 π‘Ž = 1 4 and π‘Ž 𝑏 = 7 .

  • A 1 2
  • B1
  • C 2 7
  • D 7 2
  • E2

Q15:

What is the first step in solving the equation 1 . 3 𝑦 = 1 1 . 6 ?

  • Asubtracting 1.3 from each side
  • Bmultiplying each side by 1.3
  • Cadding 1.3 to each side
  • Ddividing each side by 1.3
  • Edividing each side by 11.6

Q16:

Find the solution set of π‘₯ 3 = 3 0 in β„• .

  • A  1 1 0 
  • B βˆ…
  • C { 1 0 }
  • D { 9 0 }

Q17:

Use the diagram to solve the equation 𝑝 3 = 2 8 5 .

Q18:

Solve π‘₯ 5 = 1 0 .

  • A π‘₯ = 5
  • B π‘₯ = 2
  • C π‘₯ = 1 0
  • D π‘₯ = 5 0
  • E π‘₯ = βˆ’ 5 0

Q19:

The equation 𝑛 4 = 5 2 can be solved using the area model of multiplication as shown.

Which of the following calculations can be used to find 𝑛 ?

  • A 4 Γ· 5 2
  • B 5 2 Γ· 4
  • C 5 2 + 4
  • D 5 2 Γ— 4
  • E 5 2 βˆ’ 4

What is the value of 𝑛 ?

Q20:

What is the first step in solving the equation 𝑏 Γ· 7 = βˆ’ 1 6 8 ?

  • Asubtracting 7 from each side
  • Bdividing each side by 7
  • Cadding 7 to each side
  • Dmultiplying each side by 7
  • Emultiplying each side by 168

Q21:

How many solutions can a linear equation with variable π‘₯ have? Pick all possible answers.

  1. 0 solutions
  2. 1 solution
  3. more than 3 solutions
  4. 2 solutions
  • Aa, b
  • Ba only
  • Cb, c
  • Da, b, c
  • Eb only

Q22:

Which of the following has the same solution as π‘₯ βˆ’ 2 = βˆ’ 5 ?

  • A π‘₯ βˆ’ ( βˆ’ 2 ) = 5
  • B π‘₯ βˆ’ ( βˆ’ 2 ) = βˆ’ 5
  • C π‘₯ + ( βˆ’ 2 ) = 5
  • D π‘₯ + ( βˆ’ 2 ) = βˆ’ 5

Q23:

Solve the following equation mentally: 1 2 Γ· π‘š = 2 .

Q24:

Solve π‘₯ + 2 = 3 3 + 2 .

  • A π‘₯ = 3 5
  • B π‘₯ = 2
  • C π‘₯ = 3 1
  • D π‘₯ = 3 3
  • E π‘₯ = 8

Q25:

Which of the following addition equations have 5 as their solution?

  • A 3 2 = 2 7 + π‘₯ , 4 4 = 4 9 + π‘₯
  • B 2 7 = 3 2 + π‘₯ , 4 4 = 4 9 + π‘₯
  • C 2 7 = 3 2 + π‘₯ , 4 9 = 4 4 + π‘₯
  • D 3 2 = 2 7 + π‘₯ , 4 9 = 4 4 + π‘₯
  • E 3 2 = 2 7 + π‘₯ , 2 7 = 3 2 + π‘₯