Solve the System of Inequalities -x-12>-2 and 5(x-3)+6x>-14

$- x - 12 > - 2$ and $5 (x - 3) + 6 x > - 14$

Step 1

Simplify the first inequality.

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

Add $12$ to both sides of the inequality.

$- x > - 2 + 12$ and $5 (x - 3) + 6 x > - 14$

Add $- 2$ and $12$ .

$- x > 10$ and $5 (x - 3) + 6 x > - 14$

Divide each term in $- x > 10$ by $- 1$ and simplify.

Divide each term in $- x > 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{10}{- 1}$ and $5 (x - 3) + 6 x > - 14$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{10}{- 1}$ and $5 (x - 3) + 6 x > - 14$

Divide $x$ by $1$ .

$x < \frac{10}{- 1}$ and $5 (x - 3) + 6 x > - 14$

Simplify the right side.

Divide $10$ by $- 1$ .

$x < - 10$ and $5 (x - 3) + 6 x > - 14$

Step 2

Simplify the second inequality.

Simplify $5 (x - 3) + 6 x$ .

Simplify each term.

Apply the distributive property.

$x < - 10$ and $5 x + 5 \cdot - 3 + 6 x > - 14$

Multiply $5$ by $- 3$ .

$x < - 10$ and $5 x - 15 + 6 x > - 14$

Add $5 x$ and $6 x$ .

$x < - 10$ and $11 x - 15 > - 14$

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

Add $15$ to both sides of the inequality.

$x < - 10$ and $11 x > - 14 + 15$

Add $- 14$ and $15$ .

$x < - 10$ and $11 x > 1$

Divide each term in $11 x > 1$ by $11$ and simplify.

Divide each term in $11 x > 1$ by $11$ .

$x < - 10$ and $\frac{11 x}{11} > \frac{1}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$x < - 10$ and $\frac{11 x}{11} > \frac{1}{11}$

Divide $x$ by $1$ .

$x < - 10$ and $x > \frac{1}{11}$

Step 3

The intersection consists of the elements that are contained in both intervals.

No solution

Solve the System of Inequalities -x-12>-2 and 5(x-3)+6x>-14

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