Solve the Inequality for x 1/3x-3<-1 5/6

$\frac{1}{3} x - 3 < - 1 \frac{5}{6}$

Simplify the left side.

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} - 3 < - 1 \frac{5}{6}$

Simplify the right side.

Convert $1 \frac{5}{6}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{x}{3} - 3 < - (1 + \frac{5}{6})$

Add $1$ and $\frac{5}{6}$ .

Write $1$ as a fraction with a common denominator.

$\frac{x}{3} - 3 < - (\frac{6}{6} + \frac{5}{6})$

Combine the numerators over the common denominator.

$\frac{x}{3} - 3 < - \frac{6 + 5}{6}$

Add $6$ and $5$ .

$\frac{x}{3} - 3 < - \frac{11}{6}$

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$\frac{x}{3} < - \frac{11}{6} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{3} < - \frac{11}{6} + 3 \cdot \frac{6}{6}$

Combine $3$ and $\frac{6}{6}$ .

$\frac{x}{3} < - \frac{11}{6} + \frac{3 \cdot 6}{6}$

Combine the numerators over the common denominator.

$\frac{x}{3} < \frac{- 11 + 3 \cdot 6}{6}$

Simplify the numerator.

Multiply $3$ by $6$ .

$\frac{x}{3} < \frac{- 11 + 18}{6}$

Add $- 11$ and $18$ .

$\frac{x}{3} < \frac{7}{6}$

Multiply both sides by $3$ .

$\frac{x}{3} \cdot 3 < \frac{7}{6} \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x}{3} \cdot 3 < \frac{7}{6} \cdot 3$

Rewrite the expression.

$x < \frac{7}{6} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$x < \frac{7}{3 (2)} \cdot 3$

Cancel the common factor.

$x < \frac{7}{3 \cdot 2} \cdot 3$

Rewrite the expression.

$x < \frac{7}{2}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{7}{2}$

Interval Notation:

$(- \infty, \frac{7}{2})$

Solve the Inequality for x 1/3x-3<-1 5/6

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