Inequalities#5

$7-9z>-4z-3$

or, $7+3>-4z+9z$

or, $10>5z$

or, $2>z$

or, $z<2$

$7 - 9z > -4z - 3$

Add $9z$ to both sides:

$7 - 9z + 9z > -4z - 3 + 9z$

$⇒ 7 > 5z - 3$

Add 3 to both sides:

$⇒ 7 + 3 > 5z - 3 + 3$

$⇒ 10 > 5z$

Divide both sides by 5:

$⇒\dfrac{10}{5} > \dfrac{5z}{5}$

$⇒ 2 > z$

Swap sides:

$⇒ z < 2$