Question

Solve the inequalities for real x for the following equation: $\frac{x}{3} \ \textgreater \ \frac{x}{2} +1$.

Answer 1

$\dfrac{x}{3} \ \textgreater \ \dfrac{x}{2} +1$

Subtract x/2 from both sides:

$\dfrac{x}{3} - \dfrac{x}{2} \ \textgreater \ \ 1$

Combine like terms:

$-\dfrac{x}{6} \ \textgreater \ \ 1$

Multiply -6 on both sides:

$x \ \textless \ \ -6$