The equation you provided is:
5p - 2(p + 1) + 3(p - 6) = 3 - (p + 2)
To solve for the variable 'p', we need to simplify the equation by following certain mathematical operations step by step.
1. Distribute the Constants:Distribute the constants outside the parentheses into the terms inside the parentheses. This involves multiplying each term inside the parentheses by the constant outside it.
Distributing -2 into (p + 1) gives you -2p - 2.
Distributing 3 into (p - 6) gives you 3p - 18.
So, the equation becomes:
5p - 2p - 2 + 3p - 18 = 3 - (p + 2)
2. Combine Like Terms:Now, combine the like terms on both sides of the equation. Like terms are those that have the same variable and exponent. On the left side, you have 5p, -2p, and 3p, which can be combined to give you 6p. On the right side, you have -p and -2, which can be combined to give you -1.
The equation now looks like:
6p - 20 = 1 - p
3. Add or Subtract to Isolate 'p': The goal is to isolate 'p' on one side of the equation. Start by adding 'p' to both sides to move all the 'p' terms to the left side:
6p + p - 20 = 1
Simplifying the left side:
7p - 20 = 1
4. Isolate 'p': Next, add 20 to both sides to move the constant term to the right side:
7p - 20 + 20 = 1 + 20
Simplifying:
7p = 21
5. Solve for 'p':To solve for 'p', divide both sides of the equation by 7:
7p / 7 = 21 / 7
This gives you:
p = 3
So, the solution to the equation is p = 3. This means that if you substitute 'p' with 3 in the original equation, both sides of the equation will be equal.