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Chapter 2: Problem 45

Solve each equation, and check your solution. $$ 5 p=4 p $$

Short Answer

Expert verified
The solution is \( p = 0 \).

Step by step solution

01

Subtract the same term from both sides

Start by subtracting 4p from both sides of the equation to isolate the variable on one side. \( 5p - 4p = 4p - 4p \)
02

Simplify the equation

Simplify both sides by performing the subtraction: \[ p = 0 \]
03

Check the solution

Substitute your solution back into the original equation to ensure it is correct. \[ 5(0) = 4(0) \] which simplifies to \[ 0 = 0 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables
To solve a linear equation, one of the key steps is isolating the variable. This means getting the variable by itself on one side of the equation. Let's take our example equation 5p = 4p. Initially, it may seem challenging, but breaking it down into steps makes it simple.

First, we want to eliminate the term involving the variable from one side. In this case, we subtract 4p from both sides:
5p - 4p = 4p - 4p.
This leaves us with:
p = 0.
Now, we have successfully isolated the variable p on one side of the equation. This makes it easier to solve for p.
Simplifying Algebraic Expressions
Simplifying algebraic expressions is a crucial step in solving equations. It involves combining like terms and performing arithmetic operations. In our example, after isolating the variable, we had:
5p - 4p = 0.
It's important to perform the subtraction correctly:
(5p - 4p) = p.

Thus, we simplify our expression to p = 0. By doing so, we make the equation straightforward. Remember, simplifying helps us see the solution clearer and ensures accuracy in our calculations.
Checking Solutions
After solving the equation, it's essential to check the solution to confirm its correctness. To do this, substitute the solution back into the original equation. In our case, we found p = 0.
Let's substitute this back into the original equation 5p = 4p:
5(0) = 4(0).

This simplifies to:
0 = 0.

Because both sides of the equation are equal, our solution is verified as correct.
Checking solutions ensures that we haven't made any errors during the solving process, giving us confidence in our final answer.

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