Solve the following inequalities algebraically. Express the answer in interval notation and graph the solution set on a number line.
x/x+3>2
To clarify the problem, the first x is the numerator and the x+3 is the denominator.
Solve the following inequalities algebraically. Express the answer in interval notation and graph the solution set on a number line.
x/x+3>2
To clarify the problem, the first x is the numerator and the x+3 is the denominator.
$\displaystyle \begin{aligned}
\frac{x}
{{x + 3}} - 2 &> 0\\
\frac{{x - 2(x + 3)}}
{{x + 3}} &> 0\\
\frac{{x - 2x - 6}}
{{x + 3}} &> 0 \\
- \frac{{x + 6}}
{{x + 3}} &> 0\\
\frac{{x + 6}}
{{x + 3}} &< 0.
\end{aligned}$
We require that $\displaystyle x+6<0$ & $\displaystyle x+3>0$ or $\displaystyle x+6>0$ & $\displaystyle x+3<0.$