Finish the work to solve the equation and find the value for [tex]$p$[/tex].

[tex]2.5(-3p - 8) + 5p = 4(2.25p + 5.5) + 15.5[/tex]

1. Use the distributive property:

[tex]-7.5p - 20 + 5p = 9p + 22 + 15.5[/tex]

2. Combine like terms on each side:

[tex]-2.5p - 20 = 9p + 37.5[/tex]

Use the properties of equality to finish solving the equation. What is the value for [tex]$p$[/tex]?

[tex]p = [/tex]



Answer :

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.