The sign flip that costs SAT points: moving terms across the equals sign
If 3x − 7 = 14 and you got x = 7/3, you subtracted 7 when you should have added it.
Why it happens
Under time pressure, "move the 7 over" becomes a mechanical token-shuffle and the sign flip gets lost. The −7 must become +7 on the other side.
See the trap
If 3x − 7 = 14, what is x?
✗ The trap: 3x = 14 − 7 = 7 → x = 7/3.
✓ The fix: 3x = 14 + 7 = 21 → x = 7.
How to actually fix it
- Say the operation out loud: "add 7 to both sides", not "move the 7".
- Write the +7/−7 on BOTH sides for one line before simplifying.
- Sanity-check by substituting your answer back.
Made this mistake on a real question?
Practice Algebra questions here. Miss one and it is logged with the exact error, then brought back until you beat it.
Practice Algebra →FAQ
Is this just carelessness?
Partly — but careless errors cluster on specific operations. If sign flips are your cluster, targeted retesting fixes them faster than "be more careful".
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.