Solving linear equations

To solve equations, you need to be careful of the order you do it. Deal with the plus and minuses first, then deal with the multiplications and divisions.

Solve linear equation

\[2x+3=11\]

We must deal with the \(+3\) first. The inverse (or opposite) of \(+3\) is \(-3\). We must do this to both sides though.

\[2x+3-3=11-3\]

\[2x=8\]

The inverse (or opposite) of \(\times 2\) is \(\div 2\).

\[2x \div 2=8 \div 2\]

\[x=4\]

Solve equation with a division

\[\frac{x}{5}-2=3\]

We must deal with the \(-2\) first. The inverse (or opposite) of \(-2\) is \(+2\).

\[\frac{x}{5}-2+2=3+2\]

\[\frac{x}{5}=5\]

The inverse (or opposite) of \(\div 5\) is \(\times 5\).

\[\frac{x}{5} \times 5=5 \times 5\]

\[x=25\]

Solve equation with full fraction

\[\frac{x+2}{3}=10\]

It may be tempting to deal with the \(+2\) first, but it is trapped inside a fraction. We must always deal with brackets and fractions first.

\[\frac{x+2}{3}\times 3=10 \times 3\]

\[x+2=30\]

\[x+2-2=30-2\]

\[x=28\]