Solve the System of Inequalities 6b<24 or 4b+12>4

$6 b < 24$ or $4 b + 12 > 4$

Step 1

Divide each term in $6 b < 24$ by $6$ and simplify.

Divide each term in $6 b < 24$ by $6$ .

$\frac{6 b}{6} < \frac{24}{6}$ or $4 b + 12 > 4$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 b}{6} < \frac{24}{6}$ or $4 b + 12 > 4$

Divide $b$ by $1$ .

$b < \frac{24}{6}$ or $4 b + 12 > 4$

Simplify the right side.

Divide $24$ by $6$ .

$b < 4$ or $4 b + 12 > 4$

Step 2

Simplify the second inequality.

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

Subtract $12$ from both sides of the inequality.

$b < 4$ or $4 b > 4 - 12$

Subtract $12$ from $4$ .

$b < 4$ or $4 b > - 8$

Divide each term in $4 b > - 8$ by $4$ and simplify.

Divide each term in $4 b > - 8$ by $4$ .

$b < 4$ or $\frac{4 b}{4} > \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$b < 4$ or $\frac{4 b}{4} > \frac{- 8}{4}$

Divide $b$ by $1$ .

$b < 4$ or $b > \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$b < 4$ or $b > - 2$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5