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Lesson: Solving Equations with Rational Numbers

In this lesson, we will learn how to solve equations involving rational numbers by finding the solution set of a given linear equation.

Video

07:59

Sample Question Videos

02:02

Worksheet • 18 Questions • 1 Video

Q1:

Determine the value of π‘₯ , given that π‘₯ βˆ’ 1 1 7 = 5 1 7 .

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

Q2:

Determine the value of π‘₯ , given that π‘₯ βˆ’ 1 5 = 3 5 .

  • A 4 5
  • B 5 4
  • C βˆ’ 5 4
  • D βˆ’ 4 5

Q3:

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

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

Q4:

1 5 1 9 Γ· = 1 4 1 9 .

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

Q5:

1 4 2 7 Γ· = 1 5 6 .

  • A 2 8 9 9
  • B 7 7 8 1
  • C 1 4 7 7
  • D 3 1 5 2 8

Q6:

1 6 Γ· 4 β‹― = 1 2 .

  • A12
  • B2
  • C1
  • D4

Q7:

1 4 2 3 Γ— = 1 .

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

Q8:

Γ— 3 2 7 = 1 .

  • A 7 2 3
  • B 3 2 7
  • C 7 1 6
  • D 2 2 7

Q9:

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

  • A 400 mi
  • B 320 mi
  • C 480 mi
  • D 450 mi
  • E 350 mi

Q10:

Solve the following equation: 1 . 5 π‘₯ = βˆ’ 4 7 .

  • A π‘₯ = βˆ’ 8 2 1
  • B π‘₯ = βˆ’ 2 5 8
  • C π‘₯ = 8 2 1
  • D π‘₯ = 6 7
  • E π‘₯ = βˆ’ 6 7

Q11:

Fill in the blanks.

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

Q12:

2 4 4 4 Γ· 8 β‹― = 1 1 2 .

  • A22
  • B2
  • C3
  • D42

Q13:

Solve βˆ’ 5 7 π‘₯ = 1 7 .

  • A βˆ’ 1 5
  • B βˆ’ 5
  • C5
  • D 7 6
  • E 6 7

Q14:

Solve 5 7 π‘₯ = 4 7 .

  • A 4 5
  • B βˆ’ 5 4
  • C 5 4
  • D7
  • E βˆ’ 1 7

Q15:

Solve 3 5 π‘₯ = βˆ’ 4 5 .

  • A βˆ’ 4 3
  • B βˆ’ 3 4
  • C 3 4
  • D 5 7
  • E βˆ’ 7 5

Q16:

Solve 1 2 π‘₯ = βˆ’ 5 6 .

  • A βˆ’ 5 3
  • B βˆ’ 3 5
  • C 3 5
  • D 3 4
  • E βˆ’ 4 3

Q17:

Solve βˆ’ 3 4 π‘₯ = βˆ’ 1 8 .

  • A 1 6
  • B βˆ’ 6
  • C6
  • D 8 5
  • E 5 8

Q18:

Two students tried to solve the equation π‘₯ + 1 2 = βˆ’ 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, π‘₯ = βˆ’ 1 1 8
  • Bthe first student, π‘₯ = βˆ’ 3 8
  • Cthe first student, π‘₯ = βˆ’ 1 1 8
  • Dthe second student, π‘₯ = βˆ’ 3 8
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