Writing the inequality the wrong way round
"The Backwards Inequality"
The Mistake in Action
Solve $5 > 2x - 1$
Wrong: $6 > 2x$ $3 > x$
Therefore $x > 3$
Why It Happens
Students solve correctly but then flip the answer when writing it in the conventional form, not realizing that $3 > x$ and $x > 3$ mean completely different things.
The Fix
$3 > x$ and $x > 3$ are opposites!
- $3 > x$ means "3 is greater than $x$" → same as $x < 3$
- $x > 3$ means "$x$ is greater than 3"
Your working gives $3 > x$, which means $x < 3$.
Tip: Read the inequality aloud. "3 is greater than $x$" means $x$ must be small values (less than 3).
Spot the Mistake
Can you identify where this student went wrong?
$5 > 2x - 1$
$6 > 2x$, then $3 > x$
Therefore $x > 3$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: