Solve the System of Inequalities 16<-3x+7 or -29>-3x+7

$16 < - 3 x + 7$ or $- 29 > - 3 x + 7$

Step 1

Simplify the first inequality.

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

$- 3 x + 7 > 16$ or $- 29 > - 3 x + 7$

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

Subtract $7$ from both sides of the inequality.

$- 3 x > 16 - 7$ or $- 29 > - 3 x + 7$

Subtract $7$ from $16$ .

$- 3 x > 9$ or $- 29 > - 3 x + 7$

Divide each term in $- 3 x > 9$ by $- 3$ and simplify.

Divide each term in $- 3 x > 9$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{9}{- 3}$ or $- 29 > - 3 x + 7$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{9}{- 3}$ or $- 29 > - 3 x + 7$

Divide $x$ by $1$ .

$x < \frac{9}{- 3}$ or $- 29 > - 3 x + 7$

Simplify the right side.

Divide $9$ by $- 3$ .

$x < - 3$ or $- 29 > - 3 x + 7$

Step 2

Simplify the second inequality.

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

$x < - 3$ or $- 3 x + 7 < - 29$

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

Subtract $7$ from both sides of the inequality.

$x < - 3$ or $- 3 x < - 29 - 7$

Subtract $7$ from $- 29$ .

$x < - 3$ or $- 3 x < - 36$

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.

$x < - 3$ or $\frac{- 3 x}{- 3} > \frac{- 36}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x < - 3$ or $\frac{- 3 x}{- 3} > \frac{- 36}{- 3}$

Divide $x$ by $1$ .

$x < - 3$ or $x > \frac{- 36}{- 3}$

Simplify the right side.

Divide $- 36$ by $- 3$ .

$x < - 3$ or $x > 12$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 3 or x > 12$

Interval Notation:

$(- \infty, - 3) \cup (12, \infty)$

Step 4

Solve the System of Inequalities 16<-3x+7 or -29>-3x+7

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