Worksheet: Solving Equations with Rational Numbers

In this worksheet, we will practice solving equations involving rational numbers by finding the solution set of a given linear equation.

Q1:

Determine the value of ๐‘ฅ , given that ๐‘ฅ โˆ’ 1 1 7 = 5 1 7 .

  • A โˆ’ 6 1 7
  • B 1 7 6
  • C โˆ’ 1 7 6
  • D 6 1 7

Q2:

If ๐‘ฅ + 1 8 8 = 1 8 4 , then find the value of ๐‘ฅ .

Q3:

Solve โˆ’ 5 7 ๐‘ฅ = 1 7 .

  • A 6 7
  • B5
  • C 7 6
  • D โˆ’ 1 5
  • E โˆ’ 5

Q4:

1 5 1 9 รท = 1 4 1 9 .

  • A 1 4 1 5
  • B 2 1 0 3 6 1
  • C 1 1 5 1 2 1 0
  • D 1 1 1 4

Q5:

1 6 รท 4 โ‹ฏ = 1 2 .

  • A4
  • B2
  • C1
  • D12

Q6:

If 1 7 the number of eggs in a basket is 4 eggs, then the whole basket has eggs.

Q7:

Which of the following equations is equivalent to 2 3 ๐‘ฅ + 1 1 3 = 4 ?

  • A 6 ๐‘ฅ + 3 3 = 1 2
  • B 2 ๐‘ฅ + 1 1 = 4
  • C 6 ๐‘ฅ + 1 1 = 1 2
  • D 2 ๐‘ฅ + 1 1 = 1 2
  • E 6 ๐‘ฅ + 3 3 = 4

Q8:

1 4 2 3 ร— = 1 .

  • A 1 3 2 3
  • B 1 4 2 3
  • C 3 4 1
  • D 3 4 4

Q9:

2 4 4 4 รท 8 โ‹ฏ = 1 1 2 .

  • A42
  • B2
  • C3
  • D22

Q10:

Fill in the blanks.

  • A8, 9, 10
  • B8, 8, 10
  • C10, 9, 9
  • D8, 8, 9

Q11:

A lorry travelled 220 miles in 7 1 3 hours. On average, how many miles per hour did it travel?

  • A 660 mph
  • B 1 3 0 mph
  • C 3 1 3 7 mph
  • D 30 mph
  • E 9 4 2 7 mph

Q12:

Bassem drove for 5 1 5 hours at 79 miles per hour. About how many miles did he drive?

Q13:

Solve the following equation: 1 . 5 ๐‘ฅ = โˆ’ 4 7 .

  • A ๐‘ฅ = โˆ’ 6 7
  • B ๐‘ฅ = 8 2 1
  • C ๐‘ฅ = 6 7
  • D ๐‘ฅ = โˆ’ 8 2 1
  • E ๐‘ฅ = โˆ’ 2 5 8

Q14:

Two students tried to solve the equation ๐‘ฅ + 1 2 = โˆ’ 7 8 . The first student added 1 2 to both sides, while the second subtracted 1 2 from both sides. Determine which student was correct, and then solve for the variable.

  • Athe second student, ๐‘ฅ = โˆ’ 3 8
  • Bthe first student, ๐‘ฅ = โˆ’ 3 8
  • Cthe first student, ๐‘ฅ = โˆ’ 1 1 8
  • Dthe second student, ๐‘ฅ = โˆ’ 1 1 8

Q15:

When 4 ๐‘ฅ โˆ’ 1 3 is added to ๐‘ฅ + 2 3 , the answer is 0. What is the value of ๐‘ฅ ?

  • A 2 1 5
  • B 1 3
  • C โˆ’ 4 1 5
  • D โˆ’ 1 1 5
  • E 2 3

Q16:

Solve 2 ๐‘ง + 1 2 = 5 for ๐‘ง .

  • A 5 2
  • B 2 3 4
  • C5
  • D 2 1 4
  • E 1 1 4

Q17:

Lucy rode the bus to work today. She travelled 1 7 8 miles and, due to bad traffic, it took 3 4 of an hour. Solve the equation 3 4 ๐‘  = 1 7 8 to find the average speed ๐‘  of the bus.

  • A 1 1 8 mph
  • B 5 8 mph
  • C 1 3 4 mph
  • D 2 1 2 mph
  • E 4 3 8 mph

Q18:

Which of the following equations is equivalent to 8 9 ๐‘ฅ + 2 5 = 1 3 1 5 ?

  • A 4 0 ๐‘ฅ + 1 0 = 6 5
  • B 4 0 ๐‘ฅ + 6 = 3 9
  • C 4 0 ๐‘ฅ + 1 0 = 3 9
  • D 4 0 ๐‘ฅ + 1 8 = 3 9
  • E 4 0 ๐‘ฅ + 1 8 = 6 5

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