Problem 32 Solve. $$ p+14=83 $$... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 4: Problem 32

Solve. $$ p+14=83 $$

Short Answer

Expert verified

p = 69

Step by step solution

- Understand the Equation

The given equation is a linear equation in one variable: o p + 14 = 83. The goal is to solve for the variable p.

- Isolate the Variable

To isolate p, subtract 14 from both sides of the equation. This is based on the principle of maintaining equality by performing the same operation on both sides.

- Perform the Calculation

Subtract 14 from 83 to keep the equation balanced.p + 14 - 14 = 83 - 14Simplify the equation:p = 69

- Verify the Solution

To ensure the solution is correct, substitute p back into the original equation:p + 14 = 8369 + 14 = 83, which simplifies to 83 = 83 confirming the solution is correct.

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Key Concepts

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

Isolate the Variable

When solving a linear equation, the main goal is to isolate the variable, which means to get the variable by itself on one side of the equation. In our example, we start with the equation:

$ p + 14 = 83 $.

To isolate $ p $, we need to remove the 14 that is added to it.

We can achieve this by performing the inverse operation, which is subtraction.

Therefore, we subtract 14 from both sides of the equation.

Performing this subtraction:

$ p + 14 - 14 = 83 - 14 $

Simplifies to:

$ p = 69 $.

Now the variable $ p $ is isolated.

Principle of Maintaining Equality

A key idea in solving equations is the principle of maintaining equality. This means that whatever you do to one side of the equation, you must do to the other side to keep the equation balanced. For example, if you add, subtract, multiply, or divide one side of the equation, you must do the exact same operation on the other side.

In our example, we wanted to isolate the variable $ p $ from $ p + 14 = 83 $.

By subtracting 14 from both sides, we used the principle of maintaining equality:

$ p + 14 - 14 = 83 - 14 $.

This operation keeps the equation balanced and helps us find the correct value for $ p $.

Verify the Solution

After isolating the variable and solving the equation, it is crucial to verify the solution to ensure it is correct. Verification involves substituting the solution back into the original equation and checking if it satisfies the equation.

Let's verify our solution $ p = 69 $ for the equation $ p + 14 = 83 $:

Replace $ p $ with 69:

$ 69 + 14 = 83 $.

On simplifying:

$ 83 = 83 $.

Since both sides of the equation are equal, the solution $ p = 69 $ is verified and confirmed to be correct. This step helps you ensure that there are no mistakes in your calculations.

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91影视

Solve. $$ p+14=83 $$

Short Answer

Step by step solution

- Understand the Equation

- Isolate the Variable

- Perform the Calculation

- Verify the Solution

Key Concepts

Isolate the Variable

Principle of Maintaining Equality

Verify the Solution

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