We will learn how to solve an equation for a particular variable. The key is to move the specified variable to one side.
Steps for Solving for ○
① Move all terms other than ○ to the opposite side
② Divide both sides by the coefficient of ○
Example ①
Solve 3x + 2y = 12 for y.
Answer:2y ＝ 12 − 3x → y ＝ (12 − 3x)/2。
Solve 3x + 2y = 12 for y.
Answer:2y ＝ 12 − 3x → y ＝ (12 − 3x)/2。
Rearranging Formulas
Example ②
Solve S ＝ ah/2 for h.
Answer:2S ＝ ah → h ＝ 2S/a。
Solve S ＝ ah/2 for h.
Answer:2S ＝ ah → h ＝ 2S/a。
Example ③
Solve 5a − 2b ＝ 10 for a.
Answer:5a ＝ 10 + 2b → a ＝ (10 + 2b)/5。
Solve 5a − 2b ＝ 10 for a.
Answer:5a ＝ 10 + 2b → a ＝ (10 + 2b)/5。
Key Points
- Put the desired variable on the left and the other terms on the right
- Change the sign when moving a term
- Divide by the coefficient at the end
- A fractional form is also an acceptable answer
Practice Problems
- Solve 2x + 3y = 6 for x.
- Solve S = ab for b.
- Solve 4a − b = 2c for b.
Answers and Explanations
- Answer:x = (6 − 3y)/2
Explanation: 2x=6−3y、÷2。 - Answer:b = S/a
Explanation:Divide both sides by a。 - Answer:b = 4a − 2c
Explanation:−b=2c−4a、multiply both sides by (−1)。