Convert to Set Notation 2(3-x)>=4x+2

$2 (3 - x) \geq 4 x + 2$

Step 1

Solve $x \leq \frac{2}{3}$ .

Simplify $2 (3 - x)$ .

Rewrite.

$0 + 0 + 2 (3 - x) \geq 4 x + 2$

Simplify by adding zeros.

$2 (3 - x) \geq 4 x + 2$

Apply the distributive property.

$2 \cdot 3 + 2 (- x) \geq 4 x + 2$

Multiply.

Multiply $2$ by $3$ .

$6 + 2 (- x) \geq 4 x + 2$

Multiply $- 1$ by $2$ .

$6 - 2 x \geq 4 x + 2$

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

Subtract $4 x$ from both sides of the inequality.

$6 - 2 x - 4 x \geq 2$

Subtract $4 x$ from $- 2 x$ .

$6 - 6 x \geq 2$

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

Subtract $6$ from both sides of the inequality.

$- 6 x \geq 2 - 6$

Subtract $6$ from $2$ .

$- 6 x \geq - 4$

Divide each term in $- 6 x \geq - 4$ by $- 6$ and simplify.

Divide each term in $- 6 x \geq - 4$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} \leq \frac{- 4}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} \leq \frac{- 4}{- 6}$

Divide $x$ by $1$ .

$x \leq \frac{- 4}{- 6}$

Simplify the right side.

Cancel the common factor of $- 4$ and $- 6$ .

Factor $- 2$ out of $- 4$ .

$x \leq \frac{- 2 (2)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$x \leq \frac{- 2 \cdot 2}{- 2 \cdot 3}$

Cancel the common factor.

$x \leq \frac{- 2 \cdot 2}{- 2 \cdot 3}$

Rewrite the expression.

$x \leq \frac{2}{3}$

Step 2

Use the inequality $x \leq \frac{2}{3}$ to build the set notation.

${x | x \leq \frac{2}{3}}$

Step 3

Convert to Set Notation 2(3-x)>=4x+2

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