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

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

Step 1

Simplify the first inequality.

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

Subtract $5$ from both sides of the inequality.

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

Subtract $5$ from $8$ .

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

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 $b - 4 \geq 0$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Divide $3$ by $- 3$ .

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

Step 2

Add $4$ to both sides of the inequality.

$b < - 1$ or $b \geq 4$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$b < - 1 or b \geq 4$

Interval Notation:

$(- \infty, - 1) \cup [4, \infty)$

Step 4

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

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