Solve the following linear inequalities and write the solution in interval notation.
$negative five sixths x is less than 3$

$x < - \frac{5}{2}$

$x < - \frac{18}{5}$

$x > - \frac{18}{5}$

$x > - \frac{5}{2}$

Verified step by step guidance

Start with the given inequality: $-\frac{5}{6}x < 3$.

To isolate $x$, divide both sides of the inequality by $-\frac{5}{6}$. Remember, dividing by a negative number reverses the inequality sign.

Dividing by $-\frac{5}{6}$ is the same as multiplying by its reciprocal $-\frac{6}{5}$, so multiply both sides by $-\frac{6}{5}$ and flip the inequality sign: $x > 3 \times -\frac{6}{5}$.

Multiply the right side: \$3 \times -\frac{6}{5} = -\frac{18}{5}$, so the inequality becomes $x > -\frac{18}{5}$.

Write the solution in interval notation as all $x$ values greater than $-\frac{18}{5}$, which is $\left(-\frac{18}{5}, \infty\right)$.

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Solve the following linear inequalities and write the solution in interval notation.
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