Solve the Inequality for x -1<2-x/3<1

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

Step 1

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

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

Subtract $2$ from $- 1$ .

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

Multiply each term in the inequality by $3$ .

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

Multiply $- 3$ by $3$ .

$- 9 < - \frac{x}{3} \cdot 3 < 1 \cdot 3 - 2 \cdot 3$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 9 < \frac{- x}{3} \cdot 3 < 1 \cdot 3 - 2 \cdot 3$

Cancel the common factor.

$- 9 < \frac{- x}{3} \cdot 3 < 1 \cdot 3 - 2 \cdot 3$

Rewrite the expression.

$- 9 < - x < 1 \cdot 3 - 2 \cdot 3$

Simplify each term.

Multiply $3$ by $1$ .

$- 9 < - x < 3 - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$- 9 < - x < 3 - 6$

Subtract $6$ from $3$ .

$- 9 < - x < - 3$

Step 2

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

$\frac{- 9}{- 1} > \frac{- x}{- 1} > \frac{- 3}{- 1}$

Step 3

Divide $- 9$ by $- 1$ .

$9 > \frac{- x}{- 1} > \frac{- 3}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$9 > \frac{x}{1} > \frac{- 3}{- 1}$

Step 5

Divide $x$ by $1$ .

$9 > x > \frac{- 3}{- 1}$

Step 6

Divide $- 3$ by $- 1$ .

$9 > x > 3$

Step 7

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

$3 < x < 9$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$3 < x < 9$

Interval Notation:

$(3, 9)$

Step 9

Solve the Inequality for x -1<2-x/3<1

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