2-(4p+3)=-3(p+2)-(2p+3)

Ultimately, you want the variable p on one side of the equals sign, and the value of p on the other.

First, get rid of the parenthesis by distributing.

There is an invisible -1 in front of the first and last set of parenthesis, and a one times any number is the number itself, so you are essentially distributing the negative sign. 

So you have:     2-4p-3 = -3p-6-2p-3

Next, Combine like terms.

Can you take it from there?

Simplifying
2 + -1(4p + 3) = -3(p + 2) + -1(2p + 3)

Reorder the terms:
2 + -1(3 + 4p) = -3(p + 2) + -1(2p + 3)
2 + (3 * -1 + 4p * -1) = -3(p + 2) + -1(2p + 3)
2 + (-3 + -4p) = -3(p + 2) + -1(2p + 3)

Combine like terms: 2 + -3 = -1
-1 + -4p = -3(p + 2) + -1(2p + 3)

Reorder the terms:
-1 + -4p = -3(2 + p) + -1(2p + 3)
-1 + -4p = (2 * -3 + p * -3) + -1(2p + 3)
-1 + -4p = (-6 + -3p) + -1(2p + 3)

Reorder the terms:
-1 + -4p = -6 + -3p + -1(3 + 2p)
-1 + -4p = -6 + -3p + (3 * -1 + 2p * -1)
-1 + -4p = -6 + -3p + (-3 + -2p)

Reorder the terms:
-1 + -4p = -6 + -3 + -3p + -2p

Combine like terms: -6 + -3 = -9
-1 + -4p = -9 + -3p + -2p

Combine like terms: -3p + -2p = -5p
-1 + -4p = -9 + -5p

Solving
-1 + -4p = -9 + -5p

Move all terms containing p to the left, all other terms to the right.

Add '5p' to each side of the equation.
-1 + -4p + 5p = -9 + -5p + 5p

Combine like terms: -4p + 5p = 1p
-1 + 1p = -9 + -5p + 5p

Combine like terms: -5p + 5p = 0
-1 + 1p = -9 + 0
-1 + 1p = -9

Add '1' to each side of the equation.
-1 + 1 + 1p = -9 + 1

Combine like terms: -1 + 1 = 0
0 + 1p = -9 + 1
1p = -9 + 1

Combine like terms: -9 + 1 = -8
1p = -8

Divide each side by '1'.
p = -8

Simplifying
p = -8

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.

Iagree that is the answer to the question