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‘ฅโˆ’117=517.

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

Q2:

If ๐‘ฅ+188=184, then find the value of ๐‘ฅ.

Q3:

Solve โˆ’57๐‘ฅ=17.

  • A โˆ’ 1 5
  • B 6 7
  • C โˆ’ 5
  • D 7 6
  • E5

Q4:

1 5 1 9 รท = 1 4 1 9 .

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

Q5:

1 6 รท 4 โ‹ฏ = 1 2 .

  • A4
  • B12
  • C1
  • D2

Q6:

If 17 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 23๐‘ฅ+113=4?

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

Q8:

1 4 2 3 ร— = 1 .

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

Q9:

2 4 4 4 รท 8 โ‹ฏ = 1 1 2 .

  • A3
  • B2
  • C22
  • D42

Q10:

Fill in the blanks.

  • A8, 8, 9
  • B10, 9, 9
  • C8, 9, 10
  • D8, 8, 10

Q11:

A truck traveled 220 miles in 713 hours. On average, how many miles per hour did it travel?

  • A 1 3 0 mph
  • B30 mph
  • C660 mph
  • D 9 4 2 7 mph
  • E 3 1 3 7 mph

Q12:

Jacob drove for 515 hours at 79 miles per hour. About how many miles did he drive?

Q13:

Solve the following equation: 1.5๐‘ฅ=โˆ’47.

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

Q14:

Two students tried to solve the equation ๐‘ฅ+12=โˆ’78. The first student added 12 to both sides, while the second subtracted 12 from both sides. Determine which student was correct, and then solve for the variable.

  • Athe second student, ๐‘ฅ=โˆ’118
  • Bthe second student, ๐‘ฅ=โˆ’38
  • Cthe first student, ๐‘ฅ=โˆ’38
  • Dthe first student, ๐‘ฅ=โˆ’118

Q15:

When 4๐‘ฅโˆ’13 is added to ๐‘ฅ+23, the answer is 0. What is the value of ๐‘ฅ?

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

Q16:

Solve 2๐‘ง+12=5 for ๐‘ง.

  • A 5 2
  • B5
  • C 1 1 4
  • D 2 3 4
  • E 2 1 4

Q17:

Charlotte rode the bus to work today. She traveled 178 miles and, due to bad traffic, it took 34 of an hour. Solve the equation 34๐‘ =178 to find the average speed, ๐‘ , of the bus.

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

Q18:

Which of the following equations is equivalent to 89๐‘ฅ+25=1315?

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

Q19:

Find the rational number that equals 8 if ๏€ผ45โˆ’17๏ˆรท๏€ผ1835+17๏ˆ is subtracted from it.

Q20:

Find the value of 7๐‘ฅ given 15+๐‘ฅ7=1470.

Q21:

Solve 17+๐‘ฅ=โˆ’57.

  • A 4 7
  • B โˆ’ 4 7
  • C โˆ’ 6 7
  • D 3 7
  • E 6 7

Q22:

Find the rational number that when subtracted from its additive inverse gives โˆ’112.

  • A 3 4
  • B โˆ’ 3
  • C 3
  • D โˆ’ 3 4

Q23:

Find ๐‘Ž given ๏”๐‘Ž+๏€ผโˆ’89๏ˆ๏  is the additive inverse of 1718.

  • A โˆ’ 1 1 6
  • B โˆ’ 1 7 1 8
  • C 1 1 8
  • D 1 1 6
  • E โˆ’ 1 1 8

Q24:

Solve 12+๐‘ฆ=34 for ๐‘ฆ.

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

Q25:

Noah spends 2 hours doing homework every night. On Monday, he spent ten minutes doing geography research. The rest of his time was split so that he spent twice as long on math homework as he did on his reading, and he spent the same amount of time on an essay as he did on math.

Write an equation that can be used to determine ๐‘š, the amount of time that he spent doing his math homework on Monday.

  • A 3 2 ๐‘š + ๐‘š 2 + 1 0 ๐‘š = 1 2 0
  • B 3 2 ๐‘š + ๐‘š 2 + ๐‘š + 1 0 = 1 2 0
  • C 2 ๐‘š + ๐‘š + 2 ๐‘š + 1 0 = 1 2 0
  • D ๐‘š + ๐‘š 2 + ๐‘š + 1 0 = 1 2 0
  • E 2 ๐‘š + ๐‘š + 1 0 = 1 2 0

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