Precalculus Examples

$2 - x < 3 x + 1 < 10 x$

Step 1

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

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Step 1.1

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

$2 - x - 1 < 3 x < 10 x - 1$

Step 1.2

Subtract $1$ from $2$ .

$- x + 1 < 3 x < 10 x - 1$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- x}{3} + \frac{1}{3} < \frac{3 x}{3} < \frac{10 x}{3} + \frac{- 1}{3}$

Step 3

Move the negative in front of the fraction.

$- \frac{x}{3} + \frac{1}{3} < \frac{3 x}{3} < \frac{10 x}{3} + \frac{- 1}{3}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$- \frac{x}{3} + \frac{1}{3} < \frac{3 x}{3} < \frac{10 x}{3} + \frac{- 1}{3}$

Step 4.2

Divide $x$ by $1$ .

$- \frac{x}{3} + \frac{1}{3} < x < \frac{10 x}{3} + \frac{- 1}{3}$

Step 5

Move the negative in front of the fraction.

$- \frac{x}{3} + \frac{1}{3} < x < \frac{10 x}{3} - \frac{1}{3}$

Step 6

Convert the inequality to interval notation.

$(- \frac{x}{3} + \frac{1}{3}, \frac{10 x}{3} - \frac{1}{3})$

Step 7