Common mistakes

Why do I get the wrong answer?

Each of these is a common mistake in $2x + 6 = 14$ and similar equations. The fastest way to catch any of them: put your answer back into the equation and see whether both sides are equal.

Make one on purpose in the demo The full guide

Mistakes, and what to do instead

Mistake 1 · Why do I get $x = 10$ in $2x + 6 = 14$ ?
Why it happens
You added $6$ instead of removing it: $2x = 20$ . Check: $2 \cdot 10 + 6 = 26$ , not $14$ .
What to do instead
Subtract $6$ from both sides: $2x = 8$ , so $x = 4$ .
Mistake 2 · Why do I get $x = 1$ ?
Why it happens
You divided only the $2x$ by $2$ , and the $6$ stayed: $x + 6 = 7$ .
What to do instead
Remove the $+ 6$ first, then divide: $2x = 8$ , $x = 4$ .
Mistake 3 · Why do I get $x = 8$ ?
Why it happens
That’s $2x$ , not $x$ yet: one step was left.
What to do instead
Divide both sides by $2$ : $x = 4$ .
Mistake 4 · Why do I get $7x = 12$ in $5x + 2 = 2x + 14$ ?
Why it happens
You “moved” the $2x$ across with the wrong sign.
What to do instead
Subtract $2x$ from both sides: $3x + 2 = 14$ , $3x = 12$ , $x = 4$ .
Mistake 5 · Why do I get $x = \frac{14}{3}$ in $3(x - 2) = 12$ ?
Why it happens
You multiplied only the $x$ by $3$ : $3x - 2 = 12$ .
What to do instead
Multiply every term inside the brackets by $3$ (the distributive law): $3x - 6 = 12$ , $3x = 18$ , $x = 6$ .

A check you can always do alone

Put the answer back into the original equation. If both sides are equal, it’s right: $2 \cdot 4 + 6 = 14$ . If they are not, look for the step where the two sides stopped being equal.

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