Clear brackets, combine like terms, gather the variable on one side, then undo.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Fractions first
Multiplying every term by the common denominator clears them and simplifies the rest.
Solving for a letter
A = lw solved for w is w = A/l. Nothing changes except which letter is left alone.
Check in the original
Always substitute back into the equation you were given, not into a line you wrote.
Solving for a letter is the same process
To make r the subject of A = πr²... the steps are the ones you already use: undo operations in reverse order, doing the same to both sides. The only difference is that the numbers are letters, so nothing simplifies to a single value.
Decide which letter you are solving for
Every other letter is treated as a fixed number for the duration. In d = rt solved for t, both d and r behave exactly like constants. Writing down which letter is the unknown before starting prevents a great deal of confusion.
Why rearranging is worth doing
A formula rearranged once can be used many times. Physics, finance and engineering all state relationships in one form and need them in several. Rearranging is also how you turn a formula into a function of the variable you actually control.
Check by substituting numbers
Pick numbers satisfying the original equation, then check your rearranged version gives the same relationship. If d = 60 and r = 30 give t = 2 in both forms, the rearrangement is probably right. This catches sign and division errors quickly.
Step 2: Try It Yourself
Tap and try it out.
Left side
26
Right side
26
The two bars are the same length, so there is no difference.
Step 3: Watch an Example
One step at a time.
Watch Maya Solve 3(x − 2) + 4 = 2x + 9
Maya works through a multi-step equation.
- Step 1
She distributes on the left, giving 3x − 6 + 4 = 2x + 9.
Step 4: Your Turn
Practice makes it stick.
The Equation
Problem 1 of 2
Solve 2(x + 3) = 3x − 1.
The Formula
Problem 2 of 2
A = lw with A = 48 and l = 6. What is w?
Solve and Rearrange
1 of 4
Solve 4(x − 1) = 2x + 6.
2 of 4
Solve 5x + 3 = 2x + 21.
3 of 4
P = 2l + 2w with P = 30 and l = 9. What is w?
4 of 4
Solve x/3 + 2 = 6.
Step 5: Quick Check
Show what you know.
Question 1 of 2
Solve 3(x + 4) = x + 20.
Question 2 of 2
Where should you check your answer?
What You Learned
- Clear brackets, combine, gather, then undo.
- Rearranging a formula is the same process for a different letter.
- Check in the original equation.