The key ideas
- Do the same operation to both sides of an equation.
- Combine like terms before isolating the variable.
- Translate the words first, then solve and check the result in context.
How to solve a linear equation
Distribute any factors and combine like terms first. Then use the same operation on both sides to collect the variable terms and isolate the unknown. Substitute your result into the original equation to check it.
For a word problem, define the variable and its units before writing the equation. A fixed starting amount and a per-item charge play different roles: a cost of 7 dollars plus 3 dollars per item is 3x + 7, where x is the number of items.
What if the variable cancels?
If simplifying both sides gives a true statement such as 7 = 7, every value is a solution. If it gives a false statement such as 7 = 10, there is no solution. Do not divide by a variable coefficient that has become zero.
Worked example
Solve .
- Subtract 7 from both sides: .
- Divide both sides by 3: .
Answer:
A common mistake to avoid
Changing the sign of a term without performing the same operation on both sides.
Your turn: try a free question
One question at a time from PrepSAT's approved question bank. Your answer stays in this practice session; it is not saved to account progress.
Curriculum and sources
The key ideas and worked example come from PrepSAT's reviewed lesson curriculum. These College Board resources define the SAT scope; PrepSAT is an independent practice resource and is not affiliated with College Board.