Testing equation and inequality solutions
Substitute candidates to find which values make a mathematical statement true.
Before you begin
- Evaluating expressions
- Equality and inequality symbols
Treat a solution as a truth check
An equation states that two quantities are equal. A solution is a value that makes that statement true when substituted into every occurrence of its variable. For x + 4 = 9, trying x = 5 gives 9 = 9, so five is a solution. Trying x = 4 gives 8 = 9, which is false. An expression on its own, such as x + 4, has no equality to solve.
A solution set may contain several candidates
An inequality compares quantities instead of requiring equality. More than one candidate may satisfy it, and an unrestricted inequality can have infinitely many solutions. If a question gives a list of candidates, test each one and report every value that works. Pay attention to strict symbols: x > 3 excludes 3 itself, whereas x ≥ 3 includes the boundary.
Worked example
From {1, 2, 3, 4}, find all solutions to 2x + 1 < 8.
Show the worked solution
- For x = 1 and x = 2 the left sides are 3 and 5, both below 8.
- For x = 3 the left side is 7, also below 8.
- For x = 4 the left side is 9, which is not below 8.
1, 2 and 3.
Try it yourself
Which value solves 3n = 21?
Common mistakes
- Report all valid values from the specified set.
- A strict inequality does not include its boundary.
What can you explain now?
Which values in {0, 2, 4, 6} satisfy x + 3 = 7? Which satisfy x + 3 > 7?
Compare with the explanation
Equation: 4. Inequality: 6.
The four substituted left sides are 3, 5, 7 and 9. Only 7 equals 7, and only 9 is strictly greater than 7.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗