Certainly! Let's solve the equation step-by-step starting from where you've applied the distributive property and combined the like terms.
We have:
[tex]\[ -2.5p - 20 = 9p + 37.5 \][/tex]
To isolate [tex]\( p \)[/tex], we need to get all the [tex]\( p \)[/tex]-terms on one side and the constants on the other side. First, let's eliminate the [tex]\( 9p \)[/tex] from the right side by subtracting [tex]\( 9p \)[/tex] from both sides:
[tex]\[ -2.5p - 20 - 9p = 9p + 37.5 - 9p \][/tex]
[tex]\[ -11.5p - 20 = 37.5 \][/tex]
Next, we can move the constant term [tex]\(-20\)[/tex] to the other side by adding [tex]\( 20 \)[/tex] to both sides:
[tex]\[ -11.5p - 20 + 20 = 37.5 + 20 \][/tex]
[tex]\[ -11.5p = 57.5 \][/tex]
Now, to isolate [tex]\( p \)[/tex], divide both sides by [tex]\(-11.5\)[/tex]:
[tex]\[ p = \frac{57.5}{-11.5} \][/tex]
Perform the division:
[tex]\[ p = -5 \][/tex]
Thus, the value of [tex]\( p \)[/tex] is:
[tex]\[ p = -5 \][/tex]
This completes the solution to the equation.
