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Lesson: Linear Equations with Variables on Both Sides

In this lesson, we will learn how to solve equations in which the variable is on each side of the equation.

Sample Question Videos

01:15
02:24

Worksheet • 21 Questions • 2 Videos

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:

Nabil believes the equation can have more than one solution for special values of and . Is he right? If so, what are the values?

  • Ayes, ,
  • Byes, ,
  • Cno
  • Dyes, ,

Q5:

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

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

Q6:

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

  • AThere is no solution for π‘₯
  • B π‘₯ = βˆ’ 5
  • CThere is an infinite number of solutions as the equation is always true.
  • D π‘₯ = 5
  • E π‘₯ = 1

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

Q8:

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

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

Q9:

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

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

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

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:

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

  • A25 days
  • B15 days
  • C50 days
  • D30 days
  • E13 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‘₯ .

  • A12
  • B26
  • C16
  • D20
  • E36

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

Q18:

Solve 5 π‘₯ + 1 2 = 2 π‘₯ βˆ’ 6 .

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

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

Q20:

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

  • AThere is an infinite number of solutions as the equation is always true.
  • B π‘₯ = βˆ’ 5
  • CThere is no solution for π‘₯ .
  • D π‘₯ = 5
  • E π‘₯ = 0

Q21:

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

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