Solve the Inequality for z -2z-4<-4z-7

$- 2 z - 4 < - 4 z - 7$

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

Add $4 z$ to both sides of the inequality.

$- 2 z - 4 + 4 z < - 7$

Add $- 2 z$ and $4 z$ .

$2 z - 4 < - 7$

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

Add $4$ to both sides of the inequality.

$2 z < - 7 + 4$

Add $- 7$ and $4$ .

$2 z < - 3$

Divide each term in $2 z < - 3$ by $2$ and simplify.

Divide each term in $2 z < - 3$ by $2$ .

$\frac{2 z}{2} < \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 z}{2} < \frac{- 3}{2}$

Divide $z$ by $1$ .

$z < \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$z < - \frac{3}{2}$

The result can be shown in multiple forms.

Inequality Form:

$z < - \frac{3}{2}$

Interval Notation:

$(- \infty, - \frac{3}{2})$