solve the inequality: -2<4z+10≤12

-2<4z+10≤12

subtract 10
-12 < 4z < 2
divide by 4
-3 < z < 1/2

-12<4z<=2

-3<z<=.5

Possibly... I'm not totally sure but it is a guess.

okay thanks!!

forgot the ≤

should have been
-2<4z+10≤12
subtract 10
-12 < 4z ≤ 2
divide by 4
-3 < z ≤ 1/2

chica is also correct

To solve the inequality -2 < 4z + 10 ≤ 12, we'll first isolate z.

-2 < 4z + 10 ≤ 12

Starting with the first inequality, -2 < 4z + 10, we'll subtract 10 from both sides to move the constant term to the opposite side:

-2 - 10 < 4z + 10 - 10

-12 < 4z

Next, we divide both sides by 4 to solve for z:

-12/4 < 4z/4

-3 < z

Now, let's solve the second inequality, 4z + 10 ≤ 12. We'll subtract 10 from both sides:

4z + 10 - 10 ≤ 12 - 10

4z ≤ 2

Then, divide by 4 on both sides to solve for z:

4z/4 ≤ 2/4

z ≤ 0.5

Therefore, combining both solutions, we have -3 < z ≤ 0.5.