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Worksheet: Linear Equations with Variables on Both Sides

Q1:

π‘Š 𝑋 π‘Œ 𝑍 is a rectangle where 𝑍 π‘Œ = 9 π‘₯ βˆ’ 8 and π‘Š 𝑋 = 8 π‘₯ + 1 . Find π‘Š 𝑋 .

Q2:

Find the value of π‘₯ .

Q3:

Given that 6 π‘₯ + π‘˜ + 8 = 6 π‘₯ βˆ’ 2 , find π‘˜ .

Q4:

William believes the equation π‘Ž π‘₯ + 5 = 𝑏 ( 2 π‘₯ + 2 ) can have more than one solution for special values of π‘Ž and 𝑏 . Is he right? If so, what are the values?

  • Ayes, π‘Ž = 0 , 𝑏 = 5 2
  • Byes, π‘Ž = 5 2 , 𝑏 = 5
  • Cno
  • Dyes, π‘Ž = 5 , 𝑏 = 5 2

Q5:

Find the solution set of 8 π‘₯ 3 = π‘₯ + 5 using the substitution set { 2 4 , 1 1 , 3 , 7 } .

  • A { 1 1 }
  • B { 8 }
  • C { 7 }
  • D { 3 }
  • E { 2 4 }

Q6:

Solve 3 ( 4 π‘₯ βˆ’ 1 2 ) + 8 = 1 2 π‘₯ βˆ’ 6 .

  • A π‘₯ = 1
  • BThere is an infinite number of solutions as the equation is always true.
  • C π‘₯ = 5
  • DThere is no solution for π‘₯
  • E π‘₯ = βˆ’ 5

Q7:

Find the value of 𝑛 in the equation 𝑛 ο€Ό 1 8 + 1 2  = 𝑛 Γ— 1 8 + βˆ’ 1 6 Γ— 1 2 .

  • A 5 8
  • B βˆ’ 6
  • C 2
  • D βˆ’ 1 6
  • E 1 2

Q8:

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

  • A π‘₯ = 2
  • B π‘₯ = βˆ’ 2
  • C π‘₯ = 8
  • DThere is no solution for π‘₯ .
  • E π‘₯ = βˆ’ 8

Q9:

Solve 8 βˆ’ 2 ο€Ό 3 π‘₯ 2 + 4  = βˆ’ 5 π‘₯ + 2 .

  • A π‘₯ = βˆ’ 1
  • B π‘₯ = βˆ’ 4
  • C π‘₯ = 4
  • D π‘₯ = 1
  • E π‘₯ = βˆ’ 2

Q10:

If β–³ 𝐽 𝐾 𝐿 is isosceles, where 𝐽 𝐾 β‰… 𝐾 𝐿 , 𝐽 𝐾 = 3 π‘₯ + 3 , 𝐾 𝐿 = 5 π‘₯ βˆ’ 3 , and 𝐿 𝐽 = 4 π‘₯ + 2 , find the length of each side.

  • A 𝐽 𝐾 = 1 5 , 𝐾 𝐿 = 1 5 , 𝐿 𝐽 = 1 0
  • B 𝐽 𝐾 = 9 , 𝐾 𝐿 = 9 , 𝐿 𝐽 = 1 4
  • C 𝐽 𝐾 = 1 2 , 𝐾 𝐿 = 1 2 , 𝐿 𝐽 = 1 0
  • D 𝐽 𝐾 = 1 2 , 𝐾 𝐿 = 1 2 , 𝐿 𝐽 = 1 4
  • E 𝐽 𝐾 = 1 4 , 𝐾 𝐿 = 9 , 𝐿 𝐽 = 9

Q11:

Find the value of 𝐡 𝐢 given the following information:

  • 𝐡 is on the line between 𝐴 and 𝐢 .
  • 𝐴 𝐢 = ( 5 π‘₯ + 9 ) i n c h e s .
  • 𝐴 𝐡 = ( 3 π‘₯ βˆ’ 1 ) i n c h e s .
  • 𝐡 𝐢 = ( 3 π‘₯ + 4 ) i n c h e s .

Q12:

Point π‘Œ is the midpoint of segment 𝑋 𝑍 . Given that the length of 𝑋 π‘Œ is 2 π‘₯ βˆ’ 1 8 , and that of π‘Œ 𝑍 is 3 0 βˆ’ 2 π‘₯ , what is the length of π‘Œ 𝑍 ?

Q13:

Given that π‘š ∠ 𝐡 = π‘š ∠ 𝐢 , use the information in the figure to find the perimeter of triangle 𝐴 𝐡 𝐢 .

Q14:

Mason and Jacob are going on vacation together. Mason has $400 and Jacob has $350. Given that, on average, Mason spends $28 and Jacob spends $26 per day, after how many days will they have the same amount of money left?

  • A 13 days
  • B 50 days
  • C 30 days
  • D 25 days
  • E 15 days

Q15:

Determine the value of 𝑦 that makes the equation 6 ( π‘₯ + 8 ) + 9 π‘₯ = 𝑦 π‘₯ + 4 8 true for all values of π‘₯ .

Q16:

80 students decided to buy a present for their teacher. They split into two groups of 40 and each student in the first group gave $ π‘₯ . In the second group, three-fifths of the students gave 2 3 π‘₯ dollars each, and the rest contributed a total of $288. Given that the two groups contributed the same amount, find the value of π‘₯ .

  • A36
  • B16
  • C20
  • D12
  • E26

Q17:

The equation 2 π‘₯ + 1 0 = 5 π‘₯ + 5 can be solved in three steps. Which of the following is NOT a valid first step of such a method?

  • A Take away 5 π‘₯ from both sides.
  • B Take away 2 π‘₯ from both sides.
  • C Take away 5 from both sides.
  • D Divide both sides by 5.
  • E Take away 10 from both sides.

Q18:

Solve 5 π‘₯ + 1 2 = 2 π‘₯ βˆ’ 6 .

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

Q19:

Determine the solution set of the equation 3 ( π‘₯ βˆ’ 1 ) = π‘₯ + 9 using the substitution set { 1 5 , 1 2 , 6 , 5 } .

  • A { 1 2 }
  • B { 1 5 }
  • C { 5 }
  • D { 6 }

Q20:

Solve 4 π‘₯ + 3 2 ( 2 0 βˆ’ 8 π‘₯ ) = βˆ’ 2 π‘₯ βˆ’ 3 ( βˆ’ 1 0 + 2 π‘₯ ) .

  • A π‘₯ = 0
  • BThere is no solution for π‘₯ .
  • C π‘₯ = 5
  • DThere is an infinite number of solutions as the equation is always true.
  • E π‘₯ = βˆ’ 5

Q21:

What is the value of π‘Ž if the equation 1 2 π‘₯ = π‘Ž ( π‘₯ + 3 ) has no solutions?