Solve the Inequality for b 8-1/4b>=27

$8 - \frac{1}{4} b \geq 27$

Step 1

Combine $b$ and $\frac{1}{4}$ .

$8 - \frac{b}{4} \geq 27$

Step 2

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

Subtract $8$ from both sides of the inequality.

$- \frac{b}{4} \geq 27 - 8$

Subtract $8$ from $27$ .

$- \frac{b}{4} \geq 19$

Step 3

Divide each term in $- \frac{b}{4} \geq 19$ by $- 1$ and simplify.

Divide each term in $- \frac{b}{4} \geq 19$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{b}{4}}{- 1} \leq \frac{19}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{b}{4}}{1} \leq \frac{19}{- 1}$

Divide $\frac{b}{4}$ by $1$ .

$\frac{b}{4} \leq \frac{19}{- 1}$

Simplify the right side.

Divide $19$ by $- 1$ .

$\frac{b}{4} \leq - 19$

Step 4

Multiply both sides by $4$ .

$\frac{b}{4} \cdot 4 \leq - 19 \cdot 4$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{b}{4} \cdot 4 \leq - 19 \cdot 4$

Rewrite the expression.

$b \leq - 19 \cdot 4$

Simplify the right side.

Multiply $- 19$ by $4$ .

$b \leq - 76$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$b \leq - 76$

Interval Notation:

$(- \infty, - 76]$

Solve the Inequality for b 8-1/4b>=27

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