Solve the System of Inequalities -58<-4x-10<-14

$- 58 < - 4 x - 10 < - 14$

Step 1

Solve $- 58 < - 4 x - 10$ for $x$ .

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

$- 4 x - 10 > - 58$

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

Add $10$ to both sides of the inequality.

$- 4 x > - 58 + 10$

Add $- 58$ and $10$ .

$- 4 x > - 48$

Divide each term in $- 4 x > - 48$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 48$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- 48}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- 48}{- 4}$

Divide $x$ by $1$ .

$x < \frac{- 48}{- 4}$

Simplify the right side.

Divide $- 48$ by $- 4$ .

$x < 12$

Step 2

Solve $- 4 x - 10 < - 14$ for $x$ .

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

Add $10$ to both sides of the inequality.

$- 4 x < - 14 + 10$

Add $- 14$ and $10$ .

$- 4 x < - 4$

Divide each term in $- 4 x < - 4$ by $- 4$ and simplify.

Divide each term in $- 4 x < - 4$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $- 4$ .

$x > 1$

Step 3

Find the intersection of $x < 12$ and $x > 1$ .

$1 < x < 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 12$

Interval Notation:

$(1, 12)$

Step 5

Solve the System of Inequalities -58<-4x-10<-14

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