Solve for x -3<=(5-x)/2<7

$- 3 \leq \frac{5 - x}{2} < 7$

Step 1

Multiply each term in the inequality by $2$ .

$- 3 \cdot 2 \leq \frac{5 - x}{2} \cdot 2 < 7 \cdot 2$

Step 2

Multiply $- 3$ by $2$ .

$- 6 \leq \frac{5 - x}{2} \cdot 2 < 7 \cdot 2$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$- 6 \leq \frac{5 - x}{2} \cdot 2 < 7 \cdot 2$

Rewrite the expression.

$- 6 \leq 5 - x < 7 \cdot 2$

Step 4

Multiply $7$ by $2$ .

$- 6 \leq 5 - x < 14$

Step 5

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 - 5 \leq - x < 14 - 5$

Subtract $5$ from $- 6$ .

$- 11 \leq - x < 14 - 5$

Subtract $5$ from $14$ .

$- 11 \leq - x < 9$

Step 6

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

$\frac{- 11}{- 1} \geq \frac{- x}{- 1} > \frac{9}{- 1}$

Step 7

Divide $- 11$ by $- 1$ .

$11 \geq \frac{- x}{- 1} > \frac{9}{- 1}$

Step 8

Dividing two negative values results in a positive value.

$11 \geq \frac{x}{1} > \frac{9}{- 1}$

Step 9

Divide $x$ by $1$ .

$11 \geq x > \frac{9}{- 1}$

Step 10

Divide $9$ by $- 1$ .

$11 \geq x > - 9$

Step 11

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

$- 9 < x \leq 11$

Step 12

The result can be shown in multiple forms.

Inequality Form:

$- 9 < x \leq 11$

Interval Notation:

$(- 9, 11]$

Step 13

Solve for x -3<=(5-x)/2<7

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