Solve the System of Inequalities -3b-5>-8 or b-4<=0

$- 3 b - 5 > - 8$ or $b - 4 \leq 0$

Simplify the first inequality.

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

Add $5$ to both sides of the inequality.

$- 3 b > - 8 + 5$ or $b - 4 \leq 0$

Add $- 8$ and $5$ .

$- 3 b > - 3$ or $b - 4 \leq 0$

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

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

$\frac{- 3 b}{- 3} < \frac{- 3}{- 3}$ or $b - 4 \leq 0$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 b}{- 3} < \frac{- 3}{- 3}$ or $b - 4 \leq 0$

Divide $b$ by $1$ .

$b < \frac{- 3}{- 3}$ or $b - 4 \leq 0$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$b < 1$ or $b - 4 \leq 0$

Add $4$ to both sides of the inequality.

$b < 1$ or $b \leq 4$

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

$b \leq 4$

The result can be shown in multiple forms.

Inequality Form:

$b \leq 4$

Interval Notation:

$(- \infty, 4]$

Solve the System of Inequalities -3b-5>-8 or b-4<=0

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