Solve for z 4z-7<=-7z+9

$4 z - 7 \leq - 7 z + 9$

Step 1

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

Add $7 z$ to both sides of the inequality.

$4 z - 7 + 7 z \leq 9$

Add $4 z$ and $7 z$ .

$11 z - 7 \leq 9$

Step 2

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

Add $7$ to both sides of the inequality.

$11 z \leq 9 + 7$

Add $9$ and $7$ .

$11 z \leq 16$

Step 3

Divide each term in $11 z \leq 16$ by $11$ and simplify.

Divide each term in $11 z \leq 16$ by $11$ .

$\frac{11 z}{11} \leq \frac{16}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 z}{11} \leq \frac{16}{11}$

Divide $z$ by $1$ .

$z \leq \frac{16}{11}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z \leq \frac{16}{11}$

Interval Notation:

$(- \infty, \frac{16}{11}]$