12 - 5z/4 < 37
12-5z/4 < 37
Subtract 12 from each side.
-5z/4 < 25
Mulitply each side by -4 to cancel out the negative and 4 in the denominator. Switch the inequality symbol because you are multiplying/dividing by a negative number.
5z > -100
Divide each side by 5.
z > -20
To solve the equation 12 - (5z/4) < 37, we need to isolate the variable z.
Step 1: Subtract 12 from each side
12 - (5z/4) - 12 < 37 - 12
- (5z/4) < 25
Step 2: Multiply each side by -4
-4 * (-5z/4) > 25 * (-4)
5z > -100
Step 3: Divide each side by 5
(1/5) * 5z > (-100) / 5
z > -20
Therefore, the solution to the inequality 12 - (5z/4) < 37 is z > -20.