Solve for b 4b+18<=-12b-14<=14-5b

$4 b + 18 \leq - 12 b - 14 \leq 14 - 5 b$

Step 1

Solve $4 b + 18 \leq - 12 b - 14$ for $b$ .

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

Add $12 b$ to both sides of the inequality.

$4 b + 18 + 12 b \leq - 14$

Add $4 b$ and $12 b$ .

$16 b + 18 \leq - 14$

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

Subtract $18$ from both sides of the inequality.

$16 b \leq - 14 - 18$

Subtract $18$ from $- 14$ .

$16 b \leq - 32$

Divide each term in $16 b \leq - 32$ by $16$ and simplify.

Divide each term in $16 b \leq - 32$ by $16$ .

$\frac{16 b}{16} \leq \frac{- 32}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 b}{16} \leq \frac{- 32}{16}$

Divide $b$ by $1$ .

$b \leq \frac{- 32}{16}$

Simplify the right side.

Divide $- 32$ by $16$ .

$b \leq - 2$

Step 2

Solve $- 12 b - 14 \leq 14 - 5 b$ for $b$ .

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

Add $5 b$ to both sides of the inequality.

$- 12 b - 14 + 5 b \leq 14$

Add $- 12 b$ and $5 b$ .

$- 7 b - 14 \leq 14$

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

Add $14$ to both sides of the inequality.

$- 7 b \leq 14 + 14$

Add $14$ and $14$ .

$- 7 b \leq 28$

Divide each term in $- 7 b \leq 28$ by $- 7$ and simplify.

Divide each term in $- 7 b \leq 28$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 b}{- 7} \geq \frac{28}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 b}{- 7} \geq \frac{28}{- 7}$

Divide $b$ by $1$ .

$b \geq \frac{28}{- 7}$

Simplify the right side.

Divide $28$ by $- 7$ .

$b \geq - 4$

Step 3

Find the intersection of $b \leq - 2$ and $b \geq - 4$ .

$- 4 \leq b \leq - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq b \leq - 2$

Interval Notation:

$[- 4, - 2]$

Step 5

Solve for b 4b+18<=-12b-14<=14-5b

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