Answer:
p=6
Explanation:
Main concepts:
Concept 1. Solving a one-variable equation
Concept 2. Verification of a solution
Concept 1. Solving a one-variable equation
To solve any one variable equation, there are two main steps:
Step 1. Get the variable to show up exactly once
Step 2. Isolate the variable.
Step 1. Get the variable to show up exactly once
The variable currently only shows up once, so we can skip ahead to isolating the variable.
Step 2. Isolate the variable.
Isolating the variable usually amounts to undoing all of the things that have been done to the variable. If there are multiple things done to the variable, this will usually amount to undoing things in the reverse of the Order of Operations.
In this case, the unknown "p" is on the left side of the equation, so focus on just the left side
3p+1.8
Imagining "p" as a number, if you were to try to calculate/evaluate the value of that expression, you'd have to follow order of operations:
- first multiplying by 3, and
- then adding by 1.8
After those two steps were done, the result would be equivalent to the right side of the equation, 19.8.
In order to undo these two things, and get the p by itself, we'll need to undo those steps in reverse order:
First, undo the adding by 1.8, by subtracting 1.8 from both sides of the equation...
On the left side, whatever 3p is, it has 1.8 added to it, and then immediately subtracts 1.8. Starting with a number, and then adding and subtracting 1.8 will not change it's value, so the left side simplifies to just 3p.
Evaluating the right side of the equation, the right side simplifies to 18.
Second, we need to undo the multiplying by 3, by dividing by 3 on both sides of the equation...
Notice that here, on the left side, starting with "p", p is multiplied by 3, and then immediately divided by 3. Starting with a number, multiplying by any non-zero number, and then dividing by the same non-zero number won't change the original value, so it will simplify to just "p".
On the right, 18 over 3 evaluates to 6. So, ...
Verification
To verify an answer to an equation, substitute it back into the equation, and evaluate the left side and right side separately. If they are equal, the value is a solution to the equation. If not, something went wrong, and/or it is not a solution to the equation.
Check the left side
3p + 1.8
3(6) + 1.8
18 + 1.8
19.8
Check the right side
19.8
The left side is equal to the right side, so p=6 is a solution to the equation.