Solve the Inequality for x 1/3x+5/6x<7/3

$\frac{1}{3} x + \frac{5}{6} x < \frac{7}{3}$

Simplify $\frac{1}{3} x + \frac{5}{6} x$ .

Simplify each term.

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

$\frac{x}{3} + \frac{5}{6} x < \frac{7}{3}$

Combine $\frac{5}{6}$ and $x$ .

$\frac{x}{3} + \frac{5 x}{6} < \frac{7}{3}$

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{3} \cdot \frac{2}{2} + \frac{5 x}{6} < \frac{7}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{3 \cdot 2} + \frac{5 x}{6} < \frac{7}{3}$

Multiply $3$ by $2$ .

$\frac{x \cdot 2}{6} + \frac{5 x}{6} < \frac{7}{3}$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 5 x}{6} < \frac{7}{3}$

Simplify the numerator.

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 5 x}{6} < \frac{7}{3}$

Add $2 x$ and $5 x$ .

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

Multiply both sides by $6$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{7}{3} \cdot 6$ .

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$7 x < 7 \cdot 2$

Multiply $7$ by $2$ .

$7 x < 14$

Divide each term in $7 x < 14$ by $7$ and simplify.

Divide each term in $7 x < 14$ by $7$ .

$\frac{7 x}{7} < \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} < \frac{14}{7}$

Divide $x$ by $1$ .

$x < \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$x < 2$

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Solve the Inequality for x 1/3x+5/6x<7/3

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