Solve the Inequality for z 8+5z<=3z-7<=z+1

$8 + 5 z \leq 3 z - 7 \leq z + 1$

Solve $8 + 5 z \leq 3 z - 7$ for $z$ .

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

Subtract $3 z$ from both sides of the inequality.

$8 + 5 z - 3 z \leq - 7$

Subtract $3 z$ from $5 z$ .

$8 + 2 z \leq - 7$

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

Subtract $8$ from both sides of the inequality.

$2 z \leq - 7 - 8$

Subtract $8$ from $- 7$ .

$2 z \leq - 15$

Divide each term in $2 z \leq - 15$ by $2$ and simplify.

Divide each term in $2 z \leq - 15$ by $2$ .

$\frac{2 z}{2} \leq \frac{- 15}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 z}{2} \leq \frac{- 15}{2}$

Divide $z$ by $1$ .

$z \leq \frac{- 15}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$z \leq - \frac{15}{2}$

Solve $3 z - 7 \leq z + 1$ for $z$ .

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

Subtract $z$ from both sides of the inequality.

$3 z - 7 - z \leq 1$

Subtract $z$ from $3 z$ .

$2 z - 7 \leq 1$

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

Add $7$ to both sides of the inequality.

$2 z \leq 1 + 7$

Add $1$ and $7$ .

$2 z \leq 8$

Divide each term in $2 z \leq 8$ by $2$ and simplify.

Divide each term in $2 z \leq 8$ by $2$ .

$\frac{2 z}{2} \leq \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 z}{2} \leq \frac{8}{2}$

Divide $z$ by $1$ .

$z \leq \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$z \leq 4$

Find the intersection of $z \leq - \frac{15}{2}$ and $z \leq 4$ .

$z \leq - \frac{15}{2}$

The result can be shown in multiple forms.

Inequality Form:

$z \leq - \frac{15}{2}$

Interval Notation:

$(- \infty, - \frac{15}{2}]$

Solve the Inequality for z 8+5z<=3z-7<=z+1

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