Certainly! Let's solve the problem step-by-step:
We are given the equation:
[tex]\[ 153 = 2(z + z)n \][/tex]
First, let's simplify this equation. Notice that [tex]\(z + z\)[/tex] can be rewritten as [tex]\(2z\)[/tex], so:
[tex]\[ 153 = 2(2z)n \][/tex]
This simplifies further to:
[tex]\[ 153 = 4zn \][/tex]
We need to find the value of:
[tex]\[ 2 \cdot n \cdot (2 \cdot z) - 193 \][/tex]
To find this, let's first understand the expression involving [tex]\(z\)[/tex] and [tex]\(n\)[/tex] in our simplified equation [tex]\(153 = 4zn\)[/tex].
From the equation [tex]\(153 = 4zn\)[/tex], we solve for [tex]\(zn\)[/tex]:
[tex]\[ zn = \frac{153}{4} \][/tex]
[tex]\[ zn = 38.25 \][/tex]
Next, we substitute [tex]\(zn = 38.25\)[/tex] back into our expression to find [tex]\(2n(2z)\)[/tex].
Notice the term [tex]\(2n(2z)\)[/tex]:
[tex]\[ 2n(2z) = 2 \cdot 2 \cdot zn \][/tex]
[tex]\[ = 4 \cdot zn \][/tex]
[tex]\[ = 4 \cdot 38.25 \][/tex]
[tex]\[ = 153 \][/tex]
Now, we subtract 193 from 153:
[tex]\[ 153 - 193 = -40 \][/tex]
So, the value of [tex]\( 2 \cdot n \cdot (2 \cdot z) - 193 \)[/tex] is:
[tex]\[ \boxed{-40} \][/tex]
