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Chapter 2: Problem 406

In the following exercises, solve each equation. $$ 38=p+19 $$

Short Answer

Expert verified
p = 19

Step by step solution

01

Understand the Equation

The given equation is a simple linear equation: \[ 38 = p + 19 \]We need to solve for the variable \( p \).
02

Isolate the Variable

To isolate \( p \), we need to get rid of the constant term on the right side of the equation. We can do this by subtracting 19 from both sides of the equation.
03

Perform the Subtraction

Subtract 19 from both sides of the equation: \[ 38 - 19 = p + 19 - 19 \]This simplifies to: \[ 19 = p \]
04

Solution

We have isolated \( p \) and found that: \[ p = 19 \]

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Key Concepts

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

Isolating Variables
In algebra, one of the essential skills is isolating the variable. To 'isolate' a variable means to rearrange the equation so that the variable is by itself on one side of the equation. This helps us find the value of that variable.

In the equation given: \(38 = p + 19\)

Our goal is to get \(p\) alone. To do this, we need to remove any constants (numbers) that are added or subtracted to \(p\).

An easy way to remember this is that whatever you do to one side of the equation, you must do to the other. This keeps the equation balanced.
Performing Subtraction
Once you've decided which constant you need to get rid of to isolate your variable, the next step is to perform the subtraction.

In our equation, \(38 = p + 19\),

we need to remove the \(+19\) that is on the same side as \(p\). We do this by subtracting \(19\) from both sides:\[38 - 19 = p + 19 - 19\]

By subtracting \(19\) from both sides, we balance the equation.

This operation cancels out the \(+19\) on the right side because \(+19 - 19 = 0\). Now the equation looks like this:\[19 = p\].
Simplifying Equations
Simplifying equations helps make them easier to solve.

In our example, \[38 = p + 19\],
performed the subtraction \(38 - 19\) on both sides, and we got \(38 - 19 = 19\)

The equation simplified to: \(p = 19\).

Simplification makes it clear that \(p\) is equal to \(19\). Simple equations are easier to interpret and solve quickly.

So remember, isolating the variable, performing the right operations, and simplifying the equation are crucial steps. They help you find the solution in a structured and understandable way.

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Most popular questions from this chapter

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