Let's solve the given equation step by step:
The given equation is:
[tex]\[ 4(p x + 1) = 64 \][/tex]
### Step 1: Simplify the equation
First, divide both sides of the equation by 4 to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ p x + 1 = \frac{64}{4} \][/tex]
[tex]\[ p x + 1 = 16 \][/tex]
### Step 2: Isolate [tex]\( px \)[/tex]
Next, subtract 1 from both sides to further isolate [tex]\( px \)[/tex]:
[tex]\[ p x = 16 - 1 \][/tex]
[tex]\[ p x = 15 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex] in terms of [tex]\( p \)[/tex]
Finally, divide both sides by [tex]\( p \)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{15}{p} \][/tex]
So, the value of [tex]\( x \)[/tex] in terms of [tex]\( p \)[/tex] is:
[tex]\[ \boxed{\frac{15}{p}} \][/tex]
### Step 4: Substitute [tex]\( p = -5 \)[/tex] to find the specific value of [tex]\( x \)[/tex]
Now, substitute [tex]\( p = -5 \)[/tex] into the expression [tex]\( x = \frac{15}{p} \)[/tex]:
[tex]\[ x = \frac{15}{-5} \][/tex]
[tex]\[ x = -3 \][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\( p \)[/tex] is -5 is:
[tex]\[ \boxed{-3} \][/tex]
