Solve the System of Inequalities -12<5-x<17

$- 12 < 5 - x < 17$

Step 1

Solve $- 12 < 5 - x$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$5 - x > - 12$

Move all terms not containing $x$ to the right side of the inequality.

Subtract $5$ from both sides of the inequality.

$- x > - 12 - 5$

Subtract $5$ from $- 12$ .

$- x > - 17$

Divide each term in $- x > - 17$ by $- 1$ and simplify.

Divide each term in $- x > - 17$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{- 17}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{- 17}{- 1}$

Divide $x$ by $1$ .

$x < \frac{- 17}{- 1}$

Simplify the right side.

Divide $- 17$ by $- 1$ .

$x < 17$

Step 2

Solve $5 - x < 17$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Subtract $5$ from both sides of the inequality.

$- x < 17 - 5$

Subtract $5$ from $17$ .

$- x < 12$

Divide each term in $- x < 12$ by $- 1$ and simplify.

Divide each term in $- x < 12$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{12}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{12}{- 1}$

Divide $x$ by $1$ .

$x > \frac{12}{- 1}$

Simplify the right side.

Divide $12$ by $- 1$ .

$x > - 12$

Step 3

Find the intersection of $x < 17$ and $x > - 12$ .

$- 12 < x < 17$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 12 < x < 17$

Interval Notation:

$(- 12, 17)$

Step 5

Solve the System of Inequalities -12<5-x<17

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