Solve the System of Inequalities -3x+7>-23 OR -29>-3X+7

$- 3 x + 7 > - 23$ OR $- 29 > - 3 X + 7$

Solve $- 3 x + 7 > - 23$ for $x$ .

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

Subtract $7$ from both sides of the inequality.

$- 3 x > - 23 - 7$

Subtract $7$ from $- 23$ .

$- 3 x > - 30$

Divide each term in $- 3 x > - 30$ by $- 3$ and simplify.

Divide each term in $- 3 x > - 30$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{- 30}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{- 30}{- 3}$

Divide $x$ by $1$ .

$x < \frac{- 30}{- 3}$

Simplify the right side.

Divide $- 30$ by $- 3$ .

$x < 10$

Solve $- 29 > - 3 X + 7$ for $X$ .

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

$- 3 X + 7 < - 29$

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

Subtract $7$ from both sides of the inequality.

$- 3 X < - 29 - 7$

Subtract $7$ from $- 29$ .

$- 3 X < - 36$

Divide each term in $- 3 X < - 36$ by $- 3$ and simplify.

Divide each term in $- 3 X < - 36$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 X}{- 3} > \frac{- 36}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 X}{- 3} > \frac{- 36}{- 3}$

Divide $X$ by $1$ .

$X > \frac{- 36}{- 3}$

Simplify the right side.

Divide $- 36$ by $- 3$ .

$X > 12$

Find the intersection of $x < 10$ and $X > 12$ .

No solution

Solve the System of Inequalities -3x+7>-23 OR -29>-3X+7

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