Solve the Inequality for b 11b+6>=14b+3

$11 b + 6 \geq 14 b + 3$

Step 1

Move all terms containing $b$ to the left side of the inequality.

Subtract $14 b$ from both sides of the inequality.

$11 b + 6 - 14 b \geq 3$

Subtract $14 b$ from $11 b$ .

$- 3 b + 6 \geq 3$

Step 2

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

Subtract $6$ from both sides of the inequality.

$- 3 b \geq 3 - 6$

Subtract $6$ from $3$ .

$- 3 b \geq - 3$

Step 3

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

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

$\frac{- 3 b}{- 3} \leq \frac{- 3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 b}{- 3} \leq \frac{- 3}{- 3}$

Divide $b$ by $1$ .

$b \leq \frac{- 3}{- 3}$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$b \leq 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$b \leq 1$

Interval Notation:

$(- \infty, 1]$

Solve the Inequality for b 11b+6>=14b+3

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