Convert to Set Notation 5-3(1-x)<=3

$5 - 3 (1 - x) \leq 3$

Step 1

Solve $x \leq \frac{1}{3}$ .

Simplify $5 - 3 (1 - x)$ .

Simplify each term.

Apply the distributive property.

$5 - 3 \cdot 1 - 3 (- x) \leq 3$

Multiply $- 3$ by $1$ .

$5 - 3 - 3 (- x) \leq 3$

Multiply $- 1$ by $- 3$ .

$5 - 3 + 3 x \leq 3$

Subtract $3$ from $5$ .

$2 + 3 x \leq 3$

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

Subtract $2$ from both sides of the inequality.

$3 x \leq 3 - 2$

Subtract $2$ from $3$ .

$3 x \leq 1$

Divide each term in $3 x \leq 1$ by $3$ and simplify.

Divide each term in $3 x \leq 1$ by $3$ .

$\frac{3 x}{3} \leq \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{1}{3}$

Divide $x$ by $1$ .

$x \leq \frac{1}{3}$

Step 2

Use the inequality $x \leq \frac{1}{3}$ to build the set notation.

${x | x \leq \frac{1}{3}}$

Step 3