Definition: A two-step equation is an equation that needs two inverse operations to solve, such as 3x + 5 = 20.
What is a two-step equation?
It has a variable that has been changed by two operations, typically multiplication then addition, like 4x – 7 = 21.
How do you solve it?
Undo the operations in reverse order, working on both sides.
- Undo the addition or subtraction.
- Undo the multiplication or division.
Solve 4x – 7 = 21. Add 7 to both sides: 4x = 28. Divide both sides by 4: x = 7. Check: 4 x 7 – 7 = 21.
What about a fraction?
For n/5 + 3 = 9, subtract 3 to get n/5 = 6, then multiply by 5 to get n = 30.
Where does it appear?
A taxi charges a flat 3 dollars plus 2.50 dollars per mile. If Mathbot’s ride cost 15.50 dollars, solve 2.5m + 3 = 15.5. So 2.5m = 12.5 and m = 5 miles.
What is a common mistake?
Dividing only one term. In 3x + 6 = 21, you must divide every term by 3, or subtract 6 first. Simply writing x + 6 = 7 is wrong.
Example: 6x + 4 = 40 gives 6x = 36 and x = 6.