Solve the System of Inequalities -7x-50<=-1 AND -6x+70>-2

$- 7 x - 50 \leq - 1$ AND $- 6 x + 70 > - 2$

Solve $- 7 x - 50 \leq - 1$ for $x$ .

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

Add $50$ to both sides of the inequality.

$- 7 x \leq - 1 + 50$

Add $- 1$ and $50$ .

$- 7 x \leq 49$

Divide each term in $- 7 x \leq 49$ by $- 7$ and simplify.

Divide each term in $- 7 x \leq 49$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} \geq \frac{49}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} \geq \frac{49}{- 7}$

Divide $x$ by $1$ .

$x \geq \frac{49}{- 7}$

Simplify the right side.

Divide $49$ by $- 7$ .

$x \geq - 7$

Solve $- 6 x + 70 > - 2$ for $x$ .

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

Subtract $70$ from both sides of the inequality.

$- 6 x > - 2 - 70$

Subtract $70$ from $- 2$ .

$- 6 x > - 72$

Divide each term in $- 6 x > - 72$ by $- 6$ and simplify.

Divide each term in $- 6 x > - 72$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} < \frac{- 72}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} < \frac{- 72}{- 6}$

Divide $x$ by $1$ .

$x < \frac{- 72}{- 6}$

Simplify the right side.

Divide $- 72$ by $- 6$ .

$x < 12$

Find the intersection of $x \geq - 7$ and $x < 12$ .

$- 7 \leq x < 12$

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x < 12$

Interval Notation:

$[- 7, 12)$

Solve the System of Inequalities -7x-50<=-1 AND -6x+70>-2

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