Convert to Set Notation 1/3(x-6)>x+8

$\frac{1}{3} (x - 6) > x + 8$

Step 1

Solve $x < - 15$ .

Simplify $\frac{1}{3} (x - 6)$ .

Rewrite.

$0 + 0 + \frac{1}{3} (x - 6) > x + 8$

Simplify by adding zeros.

$\frac{1}{3} (x - 6) > x + 8$

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot - 6 > x + 8$

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

$\frac{x}{3} + \frac{1}{3} \cdot - 6 > x + 8$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$\frac{x}{3} + \frac{1}{3} \cdot (3 (- 2)) > x + 8$

Cancel the common factor.

$\frac{x}{3} + \frac{1}{3} \cdot (3 \cdot - 2) > x + 8$

Rewrite the expression.

$\frac{x}{3} - 2 > x + 8$

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

Subtract $x$ from both sides of the inequality.

$\frac{x}{3} - 2 - x > 8$

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

$\frac{x}{3} - x \cdot \frac{3}{3} - 2 > 8$

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

$\frac{x}{3} + \frac{- x \cdot 3}{3} - 2 > 8$

Combine the numerators over the common denominator.

$\frac{x - x \cdot 3}{3} - 2 > 8$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x - x \cdot 3$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 3}{3} - 2 > 8$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 3}{3} - 2 > 8$

Factor $x$ out of $- x \cdot 3$ .

$\frac{x \cdot 1 + x (- 1 \cdot 3)}{3} - 2 > 8$

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 3)$ .

$\frac{x (1 - 1 \cdot 3)}{3} - 2 > 8$

Multiply $- 1$ by $3$ .

$\frac{x (1 - 3)}{3} - 2 > 8$

Subtract $3$ from $1$ .

$\frac{x \cdot - 2}{3} - 2 > 8$

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

$\frac{- 2 \cdot x}{3} - 2 > 8$

Move the negative in front of the fraction.

$- \frac{2 x}{3} - 2 > 8$

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

Add $2$ to both sides of the inequality.

$- \frac{2 x}{3} > 8 + 2$

Add $8$ and $2$ .

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

Divide each term in $- \frac{2 x}{3} > 10$ by $- 1$ and simplify.

Divide each term in $- \frac{2 x}{3} > 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{2 x}{3}}{- 1} < \frac{10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{2 x}{3}}{1} < \frac{10}{- 1}$

Divide $\frac{2 x}{3}$ by $1$ .

$\frac{2 x}{3} < \frac{10}{- 1}$

Simplify the right side.

Divide $10$ by $- 1$ .

$\frac{2 x}{3} < - 10$

Multiply both sides by $3$ .

$\frac{2 x}{3} \cdot 3 < - 10 \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 x}{3} \cdot 3 < - 10 \cdot 3$

Rewrite the expression.

$2 x < - 10 \cdot 3$

Simplify the right side.

Multiply $- 10$ by $3$ .

$2 x < - 30$

Divide each term in $2 x < - 30$ by $2$ and simplify.

Divide each term in $2 x < - 30$ by $2$ .

$\frac{2 x}{2} < \frac{- 30}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 30}{2}$

Divide $x$ by $1$ .

$x < \frac{- 30}{2}$

Simplify the right side.

Divide $- 30$ by $2$ .

$x < - 15$

Step 2

Use the inequality $x < - 15$ to build the set notation.

${x | x < - 15}$

Step 3

Convert to Set Notation 1/3(x-6)>x+8

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