Worksheet: Linear Equations with Variables on Both Sides

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In this worksheet, we will practice solving equations in which the variable is on each side of the equation.

Q1:

Find the value of 𝑥 :

Q2:

Solve the equation − 6 ( 9 𝑥 − 2 ) − 4 ( 7 𝑥 + 1 ) = − 5 ( 2 𝑥 − 4 ) .

  • A 𝑥 = − 7 2 3
  • B 𝑥 = 1 2 4
  • C 𝑥 = − 4 4 1
  • D 𝑥 = − 1 6

Q3:

Find the value of :

Q4:

Solve the equation − 7 𝑥 + 9 = − 2 2 + 4 𝑥 .

  • A 𝑥 = 1 1 3 1
  • B 𝑥 = 1 3 3
  • C 𝑥 = 3 1 3
  • D 𝑥 = 3 1 1 1

Q5:

Given that 6 𝑥 + 𝑘 + 8 = 6 𝑥 − 2 , find 𝑘 .

Q6:

If △ 𝐽 𝐾 𝐿 is isosceles, where 𝐽 𝐾 ≅ 𝐾 𝐿 , 𝐽 𝐾 = 3 𝑥 + 3 , 𝐾 𝐿 = 5 𝑥 − 3 , and 𝐿 𝐽 = 4 𝑥 + 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

Q7:

𝑊 𝑋 𝑌 𝑍 is a rectangle where 𝑍 𝑌 = 9 𝑥 − 8 and 𝑊 𝑋 = 8 𝑥 + 1 . Find 𝑊 𝑋 .

Q8:

Find the value of 𝑥 .

Q9:

Find the value of 𝑥 :

Q10:

Find the value of 𝑥 :

Q11:

Find the value of 𝑥 :

  • A 1 4
  • B − 3 4
  • C − 1 4
  • D 3 4
  • E − 1 1 1 2 0

Q12:

Find the value of :

Q13:

Find the solution set of the equation − 5 3 + 𝑥 3 = 1 3 − 𝑥 3 .

  • A { 2 }
  • B { 6 }
  • C { 4 }
  • D { 3 }

Q14:

Find the solution set of the equation 4 1 𝑎 2 = 7 + 3 𝑎 .

  • A { 5 }
  • B { 0 . 1 }
  • C { 0 . 3 }
  • D { 0 . 4 }

Q15:

Given that 𝑚 ∠ 𝐵 = 𝑚 ∠ 𝐶 , use the information in the figure to find the perimeter of triangle 𝐴 𝐵 𝐶 .

Q16:

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?

  • A13 days
  • B50 days
  • C30 days
  • D25 days
  • E15 days

Q17:

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 $ 𝑥 . In the second group, three-fifths of the students gave 2 3 𝑥 dollars each, and the rest contributed a total of $288. Given that the two groups contributed the same amount, find the value of 𝑥 .

  • A36
  • B16
  • C20
  • D12
  • E26

Q18:

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, ,

Q19:

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

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

Q20:

Find the value of 𝐵 𝐶 given the following information:

  • 𝐵 is on the line between 𝐴 and 𝐶 .
  • 𝐴 𝐶 = ( 5 𝑥 + 9 ) i n c h e s .
  • 𝐴 𝐵 = ( 3 𝑥 − 1 ) i n c h e s .
  • 𝐵 𝐶 = ( 3 𝑥 + 4 ) i n c h e s .

Q21:

Point 𝑌 is the midpoint of segment 𝑋 𝑍 . Given that the length of 𝑋 𝑌 is 2 𝑥 − 1 8 , and that of 𝑌 𝑍 is 3 0 − 2 𝑥 , what is the length of 𝑌 𝑍 ?

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