Solving Equations — Challenge

Undo what was done, in reverse order, doing the same thing to both sides every time.

What these problems cover

These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

Solve 3x+7=22.

  1. 3
  2. 5
  3. 7
  4. 9
  5. 15
Worked answer

5

Undo the addition first: subtract 7 from both sides to get 3x = 15.

Then undo the multiplication: divide both sides by 3 to get x = 5.

Check: 3(5)+7 = 22.

Problem 2

Solve 2(x-3)=14.

  1. 4
  2. 7
  3. 8
  4. 10
  5. 11
Worked answer

10

Divide both sides by 2 first: x-3 = 7.

Add 3 to both sides: x = 10.

Check: 2(10-3) = 2· 7 = 14.

Problem 3

Solve 5x-4=3x+10.

  1. 3
  2. 5
  3. 7
  4. 9
  5. 14
Worked answer

7

Collect the x terms on one side: subtract 3x from both sides to get 2x-4 = 10.

Add 4 to both sides: 2x = 14, so x = 7.

Check: 5(7)-4 = 31 and 3(7)+10 = 31.

Problem 4

Solve x3+x4=7.

  1. 6
  2. 9
  3. 12
  4. 14
  5. 21
Worked answer

12

Combine the left side over the common denominator 12: 4x12+3x12 = 7x12.

So 7x12 = 7, which gives 7x = 84 and x = 12.

Check: 123+124 = 4+3 = 7.

Problem 5

Solve x-8=-3.

  1. -11
  2. -5
  3. 5
  4. 11
  5. 24
Worked answer

5

Add 8 to both sides: x = -3+8.

-3+8 = 5, so x = 5.

Check: 5-8 = -3.

Problem 6

The sum of two numbers is 24 and their difference is 16. What is the larger number?

  1. 4
  2. 8
  3. 16
  4. 20
  5. 22
Worked answer

20

Call the numbers a and b with a+b = 24 and a-b = 16.

Adding the two equations eliminates b: 2a = 40, so a = 20.

Then b = 4. Check: 20+4 = 24 and 20-4 = 16.

Problem 7

Solve 4(2x+1)-3x=24.

  1. 2
  2. 3
  3. 4
  4. 5
  5. 6
Worked answer

4

Expand the bracket: 8x+4-3x = 24.

Collect like terms: 5x+4 = 24, so 5x = 20 and x = 4.

Check: 4(8+1)-12 = 36-12 = 24.

Problem 8

Solve 6x=-42.

  1. -7
  2. -6
  3. 6
  4. 7
  5. -36
Worked answer

-7

Divide both sides by 6: x = -426.

A negative divided by a positive is negative, so x = -7.

Check: 6(-7) = -42.

Problem 9

A number is tripled and then increased by 5, giving 26. What is the number?

  1. 5
  2. 7
  3. 9
  4. 10
  5. 21
Worked answer

7

Translate the sentence in the order it is written: 3n+5 = 26.

Subtract 5: 3n = 21, so n = 7.

Check: tripling 7 gives 21, and 21+5 = 26.

Problem 10

Three consecutive whole numbers add to 51. What is the largest of them?

  1. 16
  2. 17
  3. 18
  4. 19
  5. 20
Worked answer

18

Call the middle number n, so the three numbers are n-1, n and n+1.

Their sum is 3n, which equals 51, so n = 17 and the numbers are 16, 17 and 18.

The largest is 18. Naming the middle number is what makes the sum collapse to 3n.

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