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Worksheet: Addition and Subtraction Equations

Q1:

Over a week, Madison practiced on her flute for 5 hours. This was 3 hours longer than she practiced the previous week. First write an equation for the number of hours ( 𝑀 ) that she spent practicing the previous week, and then solve it.

  • A 𝑀 5 = 3 1 5 ,
  • B 5 = 𝑀 βˆ’ 3 8 ,
  • C 5 = 𝑀 + 3 8 ,
  • D 5 = 𝑀 + 3 2 ,
  • E 5 = 𝑀 βˆ’ 3 2 ,

Q2:

Which of the following equations does NOT belong with the others?

  • A βˆ’ 1 0 + π‘₯ = βˆ’ 1 5
  • B 1 + π‘₯ = βˆ’ 4
  • C βˆ’ 3 + π‘₯ = βˆ’ 8
  • D 1 + π‘₯ = 5

Q3:

Find the solution set of the equation π‘₯ βˆ’ 2 0 = √ 3 8 in ℝ .

  • A  2 0 βˆ’ √ 3 8 
  • B  √ 3 8 βˆ’ 2 0 
  • C  βˆ’ 2 0 βˆ’ √ 3 8 
  • D  √ 3 8 + 2 0 

Q4:

The diagram represents the equation 2 2 = 𝑔 + 8 .

Which of the following calculations can be used to find 𝑔 ?

  • A 𝑔 = 2 2 Γ· 8
  • B 𝑔 = 2 2 + 8
  • C 𝑔 = 2 Γ— 8
  • D 𝑔 = 2 2 βˆ’ 8

What is the value of 𝑔 ?

Q5:

Find π‘Ž given  π‘Ž + ο€Ό βˆ’ 8 9   is the additive inverse of 1 7 1 8 .

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

Q6:

The given diagram represents the equation 1 8 5 = π‘₯ + 4 4 . Determine which of the following calculations is used to find π‘₯ , and give its result.

  • A π‘₯ = 1 8 5 + 4 4 = 1 4 1
  • B π‘₯ = 1 8 5 + 4 4 = 2 2 9
  • C π‘₯ = 1 8 5 βˆ’ 4 4 = 2 2 9
  • D π‘₯ = 1 8 5 βˆ’ 4 4 = 1 4 1
  • E π‘₯ = 1 8 5 βˆ’ 4 4 = 1 2 1

Q7:

Benjamin wants to buy a hooded sweatshirt that costs $73. Suppose he had saved $28. Write an equation that represents the situation, and then solve it.

  • A 2 8 = 𝑀 βˆ’ 7 3 , $101
  • B 7 3 = 𝑀 βˆ’ 2 8 , $101
  • C 7 3 = 𝑀 + 2 8 , $101
  • D 7 3 = 𝑀 + 2 8 , $45
  • E 2 8 = 𝑀 βˆ’ 7 3 , $45

Q8:

If ( π‘₯ + 9 ) is the additive inverse of βˆ’ 3 , find π‘₯ .

Q9:

Translate the following sentence into an equation: six more than eight times a number is 46.

  • A 6 π‘₯ + 8 = 4 6
  • B 8 π‘₯ βˆ’ 6 = 4 6
  • C 6 π‘₯ βˆ’ 8 = 4 6
  • D 8 π‘₯ + 6 = 4 6
  • E 6 βˆ’ 8 π‘₯ = 4 6

Q10:

The diagram represents the equation 4 5 = 1 4 + 𝑓 .

Which of the following calculations can be used to find 𝑓 ?

  • A 𝑓 = 4 5 Γ· 1 4
  • B 𝑓 = 4 5 + 1 4
  • C 𝑓 = 4 5 Γ— 1 4
  • D 𝑓 = 4 5 βˆ’ 1 4

What is the value of 𝑓 ?

Q11:

The equation 1 6 = 3 + 𝑑 can be solved using a tape diagram as shown.

The next step to solve the equation is represented by the given diagram. Which of the following calculations is used to find the missing number?

  • A 3 βˆ’ 1 6
  • B 1 6 + 3
  • C 1 6 Γ· 3
  • D 1 6 βˆ’ 3
  • E 1 6 Γ— 3

We now have the following diagram. The value of 𝑑 is found by taking away 3 from each side of the equal sign in the diagram. What is the result?

  • A 𝑑 = 1 3
  • B 𝑑 = 3 9
  • C 𝑑 = 1 9
  • D 𝑑 = 1 6
  • E 𝑑 = 3 6

Q12:

Which of the following equations has a solution of 26?

  • A π‘š + 6 = 3 1
  • B π‘š βˆ’ 5 = 3 1
  • C π‘š βˆ’ 6 = 3 1
  • D π‘š + 5 = 3 1
  • E 5 βˆ’ π‘š = 3 1

Q13:

Find the solution set of the equation 3 . 8 5 + π‘₯ = 2 2 . 5 .

  • A { βˆ’ 1 8 . 6 5 }
  • B { 2 6 }
  • C { βˆ’ 2 6 . 3 5 }
  • D { 1 8 . 6 5 }

Q14:

Find the number which, when added to 685, gives 6 292.

Q15:

Find the solution set of π‘₯ + 6 = 5 2 in β„€ .

  • A { 3 1 }
  • B { 2 5 }
  • C { βˆ’ 1 9 }
  • D { 1 9 }
  • E { βˆ’ 3 1 }

Q16:

Given that ( π‘Ž + 3 , 𝑏 + 6 ) = ( βˆ’ 1 , 6 ) , determine the values of π‘Ž and 𝑏 .

  • A π‘Ž = 2 , 𝑏 = 0
  • B π‘Ž = 0 , 𝑏 = βˆ’ 4
  • C π‘Ž = βˆ’ 4 , 𝑏 = 1 2
  • D π‘Ž = βˆ’ 4 , 𝑏 = 0
  • E π‘Ž = βˆ’ 2 , 𝑏 = 0

Q17:

Out of 34 games, a hockey team won 28 games. Solve the equation 2 8 + 𝑔 = 3 4 to determine 𝑔 , the number of games the team lost.

Q18:

Solve for π‘₯ π‘₯ + 4 . 8 = βˆ’ 8 . 9 : .

Q19:

Solve for π‘₯ π‘₯ + 4 . 4 = 7 . 1 : .

Q20:

Solve 1 7 + π‘₯ = βˆ’ 5 7 .

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

Q21:

Solve 5 9 + π‘₯ = 7 9 .

  • A βˆ’ 2 9
  • B 9 1 2
  • C βˆ’ 9 1 2
  • D 2 9
  • E 3 9

Q22:

Suppose Victoria had a score of βˆ’ 2 8 in the second round of a certain game, making her total score after two rounds βˆ’ 1 6 . Determine her score in the first round.

Q23:

Benjamin and Anthony both threw a marble in a lake. Benjamin’s marble went 2 feet farther than Anthony’s. If Benjamin’s marble went 7 feet, write and solve an equation to determine how far Anthony’s marble went.

  • A 2 + π‘₯ = 7 , 9 ft.
  • B 7 + π‘₯ = 2 , 9 ft.
  • C 7 + π‘₯ = 2 , 5 ft.
  • D 2 + π‘₯ = 7 , 5 ft.
  • E 2 + π‘₯ = 7 , 7 ft.

Q24:

What must be added to 75 to give an answer of 158?

Q25:

Anthony’s birthday is 5 days after Daniel’s. If Anthony’s birthday is on the 19th, write an equation to determine Daniel’s day of birth, and then solve it.

  • A 5 + π‘₯ = 1 9 , 24th
  • B 1 9 + π‘₯ = 5 , 24th
  • C 1 9 + π‘₯ = 5 , 14th
  • D 5 + π‘₯ = 1 9 , 14th
  • E 5 + π‘₯ = 2 4 , 19th