Solve the System of Inequalities 5+x>=3 or 6x+1<-29

$5 + x \geq 3$ or $6 x + 1 < - 29$

Step 1

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

Subtract $5$ from both sides of the inequality.

$x \geq 3 - 5$ or $6 x + 1 < - 29$

Subtract $5$ from $3$ .

$x \geq - 2$ or $6 x + 1 < - 29$

Step 2

Simplify the second inequality.

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

Subtract $1$ from both sides of the inequality.

$x \geq - 2$ or $6 x < - 29 - 1$

Subtract $1$ from $- 29$ .

$x \geq - 2$ or $6 x < - 30$

Divide each term in $6 x < - 30$ by $6$ and simplify.

Divide each term in $6 x < - 30$ by $6$ .

$x \geq - 2$ or $\frac{6 x}{6} < \frac{- 30}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$x \geq - 2$ or $\frac{6 x}{6} < \frac{- 30}{6}$

Divide $x$ by $1$ .

$x \geq - 2$ or $x < \frac{- 30}{6}$

Simplify the right side.

Divide $- 30$ by $6$ .

$x \geq - 2$ or $x < - 5$

Step 3

The union consists of all of the elements that are contained in each interval.

$x < - 5$ or $x \geq - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 5 or x \geq - 2$

Interval Notation:

$(- \infty, - 5) \cup [- 2, \infty)$

Step 5