One-Step Equations — Challenge

An equation is a balanced scale, and whatever you do to one side you must do to the other.

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 x+7=12.

  1. 5
  2. 6
  3. 7
  4. 19
  5. 84
Worked answer

5

To undo adding 7, subtract 7 from both sides.

x = 12-7 = 5.

Check: 5+7 = 12.

Problem 2

Solve 4x=20.

  1. 4
  2. 5
  3. 16
  4. 24
  5. 80
Worked answer

5

To undo multiplying by 4, divide both sides by 4.

x = 204 = 5.

Check: 4· 5 = 20.

Problem 3

Solve x-9=3.

  1. 6
  2. 9
  3. 12
  4. 27
  5. -6
Worked answer

12

To undo subtracting 9, add 9 to both sides.

x = 3+9 = 12.

Subtracting instead would give -6, which is the common slip.

Problem 4

The line y=2x+3 is reflected across y=-x. What is the equation of the reflected line?

  1. y=x/2+3/2
  2. y=2x-3
  3. y=-2x-3
  4. y=x/2-3/2
  5. y=-x/2+3/2
Worked answer

y=x/2+3/2

Reflection sends (x,y) to (X,Y)=(-y,-x).

Substitute x=-Y and y=-X: -X=-2Y+3.

So Y=X/2+3/2.

Problem 5

Solve x5=6.

  1. 11
  2. 15
  3. 30
  4. 1.2
  5. 65
Worked answer

30

To undo dividing by 5, multiply both sides by 5.

x = 6· 5 = 30.

Dividing again would give 1.2, which goes the wrong way.

Problem 6

Solve 2x+1=13.

  1. 5
  2. 6
  3. 7
  4. 12
  5. 26
Worked answer

6

Undo the addition first: 2x = 13-1 = 12.

Then undo the multiplication: x = 122 = 6.

Check: 2· 6+1 = 13.

Problem 7

Solve 3x-4=11.

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

5

Add 4 to both sides: 3x = 15.

Divide by 3: x = 5.

Check: 3· 5-4 = 11.

Problem 8

A number plus 8 equals 21. What is the number?

  1. 12
  2. 13
  3. 14
  4. 29
  5. 168
Worked answer

13

Write the sentence as an equation: n+8 = 21.

Subtract 8 from both sides: n = 13.

Check: 13+8 = 21.

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