Question

-4 = \frac{4z - 9}{6}
-24 - \left( -9 \
ight) = 4z - 9 - \left( -9 \
ight)
\boxed{} = 4z

Explanation:

Step1: Solve the first equation for -24

Start with \(-4 = \frac{4z - 9}{6}\). Multiply both sides by 6: \(-4\times6 = 4z - 9\), so \(-24 = 4z - 9\).

Step2: Analyze the second equation

We have \(-24 - (-9) = 4z - 9 - (-9)\). Simplify left side: \(-24 + 9 = -15\). Simplify right side: \(4z - 9 + 9 = 4z\). So \(-15 = 4z\) (but we just need the left side result here, which is \(-15\) from \(-24 - (-9)=-24 + 9=-15\)). Wait, actually, let's re - check the second equation's left side calculation: \(-24-(-9)=-24 + 9=-15\), and the right side \(4z-9-(-9)=4z-9 + 9 = 4z\). So the blank should be \(-15\) (since \(-24-(-9)=-15\) and that equals \(4z\) after the right side simplifies). Wait, no, the equation is \(-24-(-9)=4z-9-(-9)\), and after simplifying both sides, the left side is \(-24 + 9=-15\) and the right side is \(4z\). So the value in the blank (the left side result) is \(-15\). But let's do it step by step for the left side:
\(-24-(-9)=-24 + 9=-15\)

Answer:

\(-15\)