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From Förberedande kurs i matematik 1

Because there is an x on both the left- and right-hand sides,

the first step is to subtract x3 from both sides,

31x−1−31x=x−31x

so as to collect x on the right-hand side

−1=32x

Then, multiply both sides by 32,

\displaystyle \frac{3}{2}\centerdot \left( -1 \right)=\frac{3}{2}\centerdot \frac{2}{3}x

so that \displaystyle {2}/{3}\; can be eliminated on the right-hand side to give us

\displaystyle -\frac{3}{2}=x