Solve the Inequality for z 3+2(2z-6)<=-8z-2-5z

$3 + 2 (2 z - 6) \leq - 8 z - 2 - 5 z$

Rewrite so $z$ is on the left side of the inequality.

$- 8 z - 2 - 5 z \geq 3 + 2 (2 z - 6)$

Subtract $5 z$ from $- 8 z$ .

$- 13 z - 2 \geq 3 + 2 (2 z - 6)$

Simplify $3 + 2 (2 z - 6)$ .

Simplify each term.

Apply the distributive property.

$- 13 z - 2 \geq 3 + 2 (2 z) + 2 \cdot - 6$

Multiply $2$ by $2$ .

$- 13 z - 2 \geq 3 + 4 z + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$- 13 z - 2 \geq 3 + 4 z - 12$

Subtract $12$ from $3$ .

$- 13 z - 2 \geq 4 z - 9$

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

Subtract $4 z$ from both sides of the inequality.

$- 13 z - 2 - 4 z \geq - 9$

Subtract $4 z$ from $- 13 z$ .

$- 17 z - 2 \geq - 9$

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

Add $2$ to both sides of the inequality.

$- 17 z \geq - 9 + 2$

Add $- 9$ and $2$ .

$- 17 z \geq - 7$

Divide each term in $- 17 z \geq - 7$ by $- 17$ and simplify.

Divide each term in $- 17 z \geq - 7$ by $- 17$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 17 z}{- 17} \leq \frac{- 7}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 z}{- 17} \leq \frac{- 7}{- 17}$

Divide $z$ by $1$ .

$z \leq \frac{- 7}{- 17}$

Simplify the right side.

Dividing two negative values results in a positive value.

$z \leq \frac{7}{17}$

The result can be shown in multiple forms.

Inequality Form:

$z \leq \frac{7}{17}$

Interval Notation:

$(- \infty, \frac{7}{17}]$

Solve the Inequality for z 3+2(2z-6)<=-8z-2-5z

Related Questions

Support LCMGCF.com by disabling your adblocker.