Solve for x 1/15

$\frac{1}{15} < \frac{5 - 3 x}{15} < \frac{2}{3}$

Split the fraction into multiple fractions.

$\frac{1}{15} < \frac{5}{15} - \frac{(3) x}{15} < \frac{2}{3}$

Reduce the expression $\frac{5}{15}$ by cancelling the common factors.

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Factor $5$ out of $5$ .

$\frac{1}{15} < \frac{5 (1)}{15} - \frac{(3) x}{15} < \frac{2}{3}$

Factor $5$ out of $15$ .

$\frac{1}{15} < \frac{5 \cdot 1}{5 \cdot 3} - \frac{(3) x}{15} < \frac{2}{3}$

Cancel the common factor.

$\frac{1}{15} < \frac{5 \cdot 1}{5 \cdot 3} - \frac{(3) x}{15} < \frac{2}{3}$

Rewrite the expression.

$\frac{1}{15} < \frac{1}{3} - \frac{(3) x}{15} < \frac{2}{3}$

Reduce the expression $\frac{(3) x}{15}$ by cancelling the common factors.

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Factor $3$ out of $(3) x$ .

$\frac{1}{15} < \frac{1}{3} - \frac{(3) (x)}{15} < \frac{2}{3}$

Factor $3$ out of $15$ .

$\frac{1}{15} < \frac{1}{3} - \frac{3 x}{3 \cdot 5} < \frac{2}{3}$

Cancel the common factor.

$\frac{1}{15} < \frac{1}{3} - \frac{3 x}{3 \cdot 5} < \frac{2}{3}$

Rewrite the expression.

$\frac{1}{15} < \frac{1}{3} - \frac{x}{5} < \frac{2}{3}$

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

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Subtract $\frac{1}{3}$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$\frac{1}{15} - \frac{1}{3} < - \frac{x}{5} < \frac{2}{3} - \frac{1}{3}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{15} - \frac{1}{3} \cdot \frac{5}{5} < - \frac{x}{5} < \frac{2}{3} - \frac{1}{3}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{1}{3}$ and $\frac{5}{5}$ .

$\frac{1}{15} - \frac{5}{3 \cdot 5} < - \frac{x}{5} < \frac{2}{3} - \frac{1}{3}$

Multiply $3$ by $5$ .

$\frac{1}{15} - \frac{5}{15} < - \frac{x}{5} < \frac{2}{3} - \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{1 - 5}{15} < - \frac{x}{5} < \frac{2}{3} - \frac{1}{3}$

Subtract $5$ from $1$ .

$\frac{- 4}{15} < - \frac{x}{5} < \frac{2}{3} - \frac{1}{3}$

Move the negative in front of the fraction.

$- \frac{4}{15} < - \frac{x}{5} < \frac{2}{3} - \frac{1}{3}$

Multiply each term in the inequality by $5$ .

$- \frac{4}{15} \cdot 5 < - \frac{x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{4}{15}$ into the numerator.

$\frac{- 4}{15} \cdot 5 < - \frac{x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Factor $5$ out of $15$ .

$\frac{- 4}{5 (3)} \cdot 5 < - \frac{x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Cancel the common factor.

$\frac{- 4}{5 \cdot 3} \cdot 5 < - \frac{x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Rewrite the expression.

$\frac{- 4}{3} < - \frac{x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Move the negative in front of the fraction.

$- \frac{4}{3} < - \frac{x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{x}{5}$ into the numerator.

$- \frac{4}{3} < \frac{- x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Cancel the common factor.

$- \frac{4}{3} < \frac{- x}{5} \cdot 5 < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Rewrite the expression.

$- \frac{4}{3} < - x < \frac{2}{3} \cdot 5 - \frac{1}{3} \cdot 5$

Simplify each term.

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Multiply $\frac{2}{3} \cdot 5$ .

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Combine $\frac{2}{3}$ and $5$ .

$- \frac{4}{3} < - x < \frac{2 \cdot 5}{3} - \frac{1}{3} \cdot 5$

Multiply $2$ by $5$ .

$- \frac{4}{3} < - x < \frac{10}{3} - \frac{1}{3} \cdot 5$

Multiply $- \frac{1}{3} \cdot 5$ .

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Multiply $5$ by $- 1$ .

$- \frac{4}{3} < - x < \frac{10}{3} - 5 (\frac{1}{3})$

Combine $- 5$ and $\frac{1}{3}$ .

$- \frac{4}{3} < - x < \frac{10}{3} + \frac{- 5}{3}$

Move the negative in front of the fraction.

$- \frac{4}{3} < - x < \frac{10}{3} - \frac{5}{3}$

Combine the numerators over the common denominator.

$- \frac{4}{3} < - x < \frac{10 - 5}{3}$

Subtract $5$ from $10$ .

$- \frac{4}{3} < - x < \frac{5}{3}$

Multiply each term in the inequality by $- 1$ .

$- \frac{4}{3} \cdot - 1 > (- x) \cdot - 1 > \frac{5}{3} \cdot - 1$

Multiply $- \frac{4}{3} \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 (\frac{4}{3}) > (- x) \cdot - 1 > \frac{5}{3} \cdot - 1$

Multiply $\frac{4}{3}$ by $1$ .

$\frac{4}{3} > (- x) \cdot - 1 > \frac{5}{3} \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$\frac{4}{3} > 1 x > \frac{5}{3} \cdot - 1$

Multiply $x$ by $1$ .

$\frac{4}{3} > x > \frac{5}{3} \cdot - 1$

Multiply $\frac{5}{3} \cdot - 1$ .

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Combine $\frac{5}{3}$ and $- 1$ .

$\frac{4}{3} > x > \frac{5 \cdot - 1}{3}$

Multiply $5$ by $- 1$ .

$\frac{4}{3} > x > \frac{- 5}{3}$

Move the negative in front of the fraction.

$\frac{4}{3} > x > - \frac{5}{3}$

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

$- \frac{5}{3} < x < \frac{4}{3}$

Solve for x 1/15<(5-3x)/15<2/3

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