Convert to Set Notation 3(x-4)-5x>=x+6

$3 (x - 4) - 5 x \geq x + 6$

Step 1

Solve $x \leq - 6$ .

Simplify $3 (x - 4) - 5 x$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 4 - 5 x \geq x + 6$

Multiply $3$ by $- 4$ .

$3 x - 12 - 5 x \geq x + 6$

Subtract $5 x$ from $3 x$ .

$- 2 x - 12 \geq x + 6$

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

Subtract $x$ from both sides of the inequality.

$- 2 x - 12 - x \geq 6$

Subtract $x$ from $- 2 x$ .

$- 3 x - 12 \geq 6$

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

Add $12$ to both sides of the inequality.

$- 3 x \geq 6 + 12$

Add $6$ and $12$ .

$- 3 x \geq 18$

Divide each term in $- 3 x \geq 18$ by $- 3$ and simplify.

Divide each term in $- 3 x \geq 18$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \leq \frac{18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \leq \frac{18}{- 3}$

Divide $x$ by $1$ .

$x \leq \frac{18}{- 3}$

Simplify the right side.

Divide $18$ by $- 3$ .

$x \leq - 6$

Step 2

Use the inequality $x \leq - 6$ to build the set notation.

${x | x \leq - 6}$

Step 3

Convert to Set Notation 3(x-4)-5x>=x+6

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