Solve Two-Stage Equations

When we solve algebraic equations, our aim is to end up with one letter on one side of the equals sign and one number on the other.  This is the solution.

 

We do this by using inverse operations to undo things that get in the way, but remember that we must do the same thing to both sides.

 

Example

5b + 3 = 23

 

Answer

Subtract 3 from both sides:

5b + 3 - 3 = 23 - 3

 

Simplify:

5b = 20

 

Divide both sides by 5:

5b ÷ 5 = 20 ÷ 5

 

Simplify:

b = 4

 

Example

b/5 - 3 = 17

 

Answer

Add 3 to both sides:

b/5 - 3 + 3 = 17 + 3

 

Simplify:

b/5 = 20

 

Multiply both sides by 5:

b ÷ 5 x 5 = 20 x 5

 

Simplify:

b = 100

 

Example

Solve for a

5 - a = 10

 

Answer

Add a to both sides:

5 - a + a = 10 + a

 

Simplify:

5 = 10 + a

 

Subtract 10 from both sides:

5 -10 = 10 - 10 + a

 

Simplify:

-5 = a

a = -5

 

Want a bit more help with this before you begin? Why not watch this short video?