Worksheet: Equations with Polynomials on Both Sides

In this worksheet, we will practice solving equations with polynomials on both sides to get a variable's value or to get the missing terms on both sides of the equation.

Q1:

Given that 1 6 ๐‘Ž ๐‘ + 2 6 ๐‘Ž = 2 ๐‘Ž ๏€น 8 ๐‘Ž ๐‘ + ๐‘˜ ๏… 5 2 4 2 , what is the value of ๐‘˜ ?

Q2:

Complete 4 ๐‘ฅ ๐‘ฆ ๏€น + โˆ’ 2 ๐‘ฅ ๏… = โˆ’ 1 2 ๐‘ฅ ๐‘ฆ + 1 2 ๐‘ฅ ๐‘ฆ + 2 3 3 4 6 2 6 .

  • A 3 ๐‘ฅ ๐‘ฆ 2 3 , โˆ’ 3 ๐‘ฆ 3 , โˆ’ 8 ๐‘ฅ ๐‘ฆ 5 3
  • B โˆ’ 3 ๐‘ฅ ๐‘ฆ 3 2 , 3 ๐‘ฆ 3 , โˆ’ 8 ๐‘ฅ ๐‘ฆ 3 5
  • C โˆ’ 3 ๐‘ฅ ๐‘ฆ 2 3 , 3 ๐‘ฆ , โˆ’ 8 ๐‘ฅ ๐‘ฆ 5 3
  • D โˆ’ 3 ๐‘ฅ ๐‘ฆ 2 3 , 3 ๐‘ฆ 3 , โˆ’ 8 ๐‘ฅ ๐‘ฆ 5 3

Q3:

Complete ๏€น โˆ’ ๐‘š ๐‘› ๏… = 3 ๐‘š ๐‘› โˆ’ ๐‘š ๐‘› 4 4 8 2 8 .

  • A 3 ๐‘š ๐‘› 4 , ๐‘š ๐‘› 4 3
  • B ๐‘š ๐‘› 4 , 3 ๐‘š ๐‘› 3 4
  • C ๐‘š ๐‘› 4 , 3 ๐‘š ๐‘› 4 3
  • D ๐‘š ๐‘› 4 , 3 ๐‘š ๐‘› 3 4

Q4:

Given that 1 8 ๐‘Ž ๐‘ โˆ’ 2 8 ๐‘Ž ๐‘ = 2 ๐‘Ž ๐‘ ( 9 ๐‘Ž ๐‘ + ๐‘˜ ) 5 4 4 3 4 3 , what is the value of ๐‘˜ ?

Q5:

Given that 2 7 ๐‘Ž ๐‘ โˆ’ 1 2 ๐‘Ž ๐‘ = 3 ๐‘Ž ๐‘ ( 9 ๐‘Ž + ๐‘˜ ) 4 3 3 , what is the value of ๐‘˜ ?

Q6:

Complete โˆ’ ๐‘ฅ ๐‘ฆ ( + โˆ’ 3 ๐‘ฅ ) = โˆ’ 3 ๐‘ฅ ๐‘ฆ โˆ’ ๐‘ฅ ๐‘ฆ + 3 3 5 6 3 5 .

  • A ๐‘ฅ ๐‘ฆ 2 3 , 3 ๐‘ฆ 2 , 3 ๐‘ฅ ๐‘ฆ 4 3
  • B 3 ๐‘ฅ ๐‘ฆ 3 2 , ๐‘ฆ 2 , 3 ๐‘ฅ ๐‘ฆ 3 4
  • C 3 ๐‘ฅ ๐‘ฆ 2 3 , ๐‘ฆ , 3 ๐‘ฅ ๐‘ฆ 4 3
  • D 3 ๐‘ฅ ๐‘ฆ 2 3 , ๐‘ฆ 2 , 3 ๐‘ฅ ๐‘ฆ 4 3

Q7:

Complete โˆ’ 2 ๐‘ฅ ๐‘ฆ ๏€น + โˆ’ 4 ๐‘ฅ ๏… = 6 ๐‘ฅ ๐‘ฆ โˆ’ 4 ๐‘ฅ ๐‘ฆ + 2 3 2 3 5 2 5 .

  • A 2 ๐‘ฅ ๐‘ฆ 2 , โˆ’ 3 ๐‘ฆ 2 , 8 ๐‘ฅ ๐‘ฆ 4 3
  • B โˆ’ 3 ๐‘ฅ ๐‘ฆ 2 , 2 ๐‘ฆ 2 , 8 ๐‘ฅ ๐‘ฆ 3 4
  • C โˆ’ 3 ๐‘ฅ ๐‘ฆ 2 , 2 ๐‘ฆ , 8 ๐‘ฅ ๐‘ฆ 4 3
  • D โˆ’ 3 ๐‘ฅ ๐‘ฆ 2 , 2 ๐‘ฆ 2 , 8 ๐‘ฅ ๐‘ฆ 4 3

Q8:

Complete ๏€น โˆ’ 5 ๐‘š ๐‘› ๏… = 2 ๐‘š ๐‘› + 1 0 ๐‘š ๐‘› 4 3 6 4 7 5 .

  • A โˆ’ ๐‘š ๐‘› 3 2 , โˆ’ 2 ๐‘š ๐‘› 2 3
  • B โˆ’ 2 ๐‘š ๐‘› 2 3 , โˆ’ ๐‘š ๐‘› 3 2
  • C โˆ’ 2 ๐‘š ๐‘› 3 2 , โˆ’ ๐‘š ๐‘› 2 3
  • D โˆ’ 2 ๐‘š ๐‘› 3 2 , โˆ’ ๐‘š ๐‘› 3 2

Q9:

Complete ๏€น โˆ’ 3 ๐‘š ๐‘› ๏… = 6 ๐‘š ๐‘› + 9 ๐‘š ๐‘› 3 3 4 5 6 4 .

  • A โˆ’ 2 ๐‘š ๐‘› 3 , โˆ’ 3 ๐‘š ๐‘› 4
  • B โˆ’ 3 ๐‘š ๐‘› 3 , โˆ’ 2 ๐‘š ๐‘› 4
  • C โˆ’ 3 ๐‘š ๐‘› 3 , โˆ’ 2 ๐‘š ๐‘› 4
  • D โˆ’ 3 ๐‘š ๐‘› 3 , โˆ’ 2 ๐‘š ๐‘› 4

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