Solve the Inequality for x x/2+x/3<5

$\frac{x}{2} + \frac{x}{3} < 5$

Simplify $\frac{x}{2} + \frac{x}{3}$ .

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

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

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

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

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

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

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

Multiply $2$ by $3$ .

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $3$ to the left of $x$ .

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

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

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

Add $3 x$ and $2 x$ .

$\frac{5 x}{6} < 5$

Multiply both sides by $6$ .

$\frac{5 x}{6} \cdot 6 < 5 \cdot 6$

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{5 x}{6} \cdot 6 < 5 \cdot 6$

Rewrite the expression.

$5 x < 5 \cdot 6$

Simplify the right side.

Multiply $5$ by $6$ .

$5 x < 30$

Divide each term in $5 x < 30$ by $5$ and simplify.

Divide each term in $5 x < 30$ by $5$ .

$\frac{5 x}{5} < \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} < \frac{30}{5}$

Divide $x$ by $1$ .

$x < \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x < 6$

The result can be shown in multiple forms.

Inequality Form:

$x < 6$

Interval Notation:

$(- \infty, 6)$

Solve the Inequality for x x/2+x/3<5

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