Equations — solving linear equations in one unknown

When splitting a side into separate fractions, students divide one term by the denominator but not the other (e.g. getting 5n + 2 from a careless split).

When multiplying both sides to remove a denominator, students multiply some terms but not others, or forget to use brackets around a multi-term side.

Moving an $x$-term or a number to the other side with the wrong sign while gathering like terms — for example adding instead of subtracting.

Linear equations often have fractional solutions, and these must be left exact. If the working gives $7x=24$, write $x=\dfrac{24}{7}$ (or $3\tfrac{3}{7}$) — rounding to a decimal throws away the accuracy mark.

When two single fractions are equal, each whole numerator multiplies the other denominator. From $\dfrac{x+2}{3}=\dfrac{2x-1}{5}$ you get $5(x+2)=3(2x-1)$; writing $5(x+2)=3 \cdot 2x-1$ drops the bracket and the answer goes wrong.