Convert to Set Notation 10>=3x-1>=0

$10 \geq 3 x - 1 \geq 0$

Solve $\frac{11}{3} \geq x \geq \frac{1}{3}$ .

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Move all terms not containing $x$ from the center section of the inequality.

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Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$10 + 1 \geq 3 x \geq 0 + 1$

Add $10$ and $1$ .

$11 \geq 3 x \geq 0 + 1$

Add $0$ and $1$ .

$11 \geq 3 x \geq 1$

Divide each term in the inequality by $3$ .

$\frac{11}{3} \geq \frac{3 x}{3} \geq \frac{1}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{11}{3} \geq \frac{3 x}{3} \geq \frac{1}{3}$

Divide $x$ by $1$ .

$\frac{11}{3} \geq x \geq \frac{1}{3}$

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$\frac{1}{3} \leq x \leq \frac{11}{3}$

Use the inequality $\frac{1}{3} \leq x \leq \frac{11}{3}$ to build the set notation.

${x | \frac{1}{3} \leq x \leq \frac{11}{3}}$

Convert to Set Notation 10>=3x-1>=0