Solve the Inequality for z 2(z+1)-4(z-4)<=2(z+5)

$2 (z + 1) - 4 (z - 4) \leq 2 (z + 5)$

Simplify $2 (z + 1) - 4 (z - 4)$ .

Simplify each term.

Apply the distributive property.

$2 z + 2 \cdot 1 - 4 (z - 4) \leq 2 (z + 5)$

Multiply $2$ by $1$ .

$2 z + 2 - 4 (z - 4) \leq 2 (z + 5)$

Apply the distributive property.

$2 z + 2 - 4 z - 4 \cdot - 4 \leq 2 (z + 5)$

Multiply $- 4$ by $- 4$ .

$2 z + 2 - 4 z + 16 \leq 2 (z + 5)$

Simplify by adding terms.

Subtract $4 z$ from $2 z$ .

$- 2 z + 2 + 16 \leq 2 (z + 5)$

Add $2$ and $16$ .

$- 2 z + 18 \leq 2 (z + 5)$

Simplify $2 (z + 5)$ .

Apply the distributive property.

$- 2 z + 18 \leq 2 z + 2 \cdot 5$

Multiply $2$ by $5$ .

$- 2 z + 18 \leq 2 z + 10$

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

Subtract $2 z$ from both sides of the inequality.

$- 2 z + 18 - 2 z \leq 10$

Subtract $2 z$ from $- 2 z$ .

$- 4 z + 18 \leq 10$

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

Subtract $18$ from both sides of the inequality.

$- 4 z \leq 10 - 18$

Subtract $18$ from $10$ .

$- 4 z \leq - 8$

Divide each term in $- 4 z \leq - 8$ by $- 4$ and simplify.

Divide each term in $- 4 z \leq - 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 z}{- 4} \geq \frac{- 8}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 z}{- 4} \geq \frac{- 8}{- 4}$

Divide $z$ by $1$ .

$z \geq \frac{- 8}{- 4}$

Simplify the right side.

Divide $- 8$ by $- 4$ .

$z \geq 2$

The result can be shown in multiple forms.

Inequality Form:

$z \geq 2$

Interval Notation:

$[2, \infty)$

Solve the Inequality for z 2(z+1)-4(z-4)<=2(z+5)

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