Solve the Inequality for x 2x-5/3>x/3+10

$2 x - \frac{5}{3} > \frac{x}{3} + 10$

Move all terms containing $x$ to the left side of the inequality.

Subtract $\frac{x}{3}$ from both sides of the inequality.

$2 x - \frac{5}{3} - \frac{x}{3} > 10$

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

$2 x \cdot \frac{3}{3} - \frac{x}{3} - \frac{5}{3} > 10$

Combine $2 x$ and $\frac{3}{3}$ .

$\frac{2 x \cdot 3}{3} - \frac{x}{3} - \frac{5}{3} > 10$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 - x}{3} - \frac{5}{3} > 10$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 - x - 5}{3} > 10$

Multiply $3$ by $2$ .

$\frac{6 x - x - 5}{3} > 10$

Subtract $x$ from $6 x$ .

$\frac{5 x - 5}{3} > 10$

Factor $5$ out of $5 x - 5$ .

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 5}{3} > 10$

Factor $5$ out of $- 5$ .

$\frac{5 (x) + 5 (- 1)}{3} > 10$

Factor $5$ out of $5 (x) + 5 (- 1)$ .

$\frac{5 (x - 1)}{3} > 10$

Multiply both sides by $3$ .

$\frac{5 (x - 1)}{3} \cdot 3 > 10 \cdot 3$

Simplify.

Simplify the left side.

Simplify $\frac{5 (x - 1)}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5 (x - 1)}{3} \cdot 3 > 10 \cdot 3$

Rewrite the expression.

$5 (x - 1) > 10 \cdot 3$

Apply the distributive property.

$5 x + 5 \cdot - 1 > 10 \cdot 3$

Multiply $5$ by $- 1$ .

$5 x - 5 > 10 \cdot 3$

Simplify the right side.

Multiply $10$ by $3$ .

$5 x - 5 > 30$

Solve for $x$ .

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

Add $5$ to both sides of the inequality.

$5 x > 30 + 5$

Add $30$ and $5$ .

$5 x > 35$

Divide each term in $5 x > 35$ by $5$ and simplify.

Divide each term in $5 x > 35$ by $5$ .

$\frac{5 x}{5} > \frac{35}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} > \frac{35}{5}$

Divide $x$ by $1$ .

$x > \frac{35}{5}$

Simplify the right side.

Divide $35$ by $5$ .

$x > 7$

The result can be shown in multiple forms.

Inequality Form:

$x > 7$

Interval Notation:

$(7, \infty)$

Solve the Inequality for x 2x-5/3>x/3+10

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