Problem 327 In the following exercises, solv... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 327

In the following exercises, solve the equation. Then check your solution. $$ p+8=-2 $$

Short Answer

Expert verified

$ p = -10 $

Step by step solution

- Isolate the variable

Start by isolating the variable $ p $. To do this, subtract 8 from both sides of the equation.

- Perform the operation

Subtract 8 from both sides:\[ p + 8 - 8 = -2 - 8 \]This simplifies to:\[ p = -10 \]

- Check the solution

Substitute $ p = -10 $ back into the original equation to check the solution:\[ -10 + 8 = -2 \]Since both sides of the equation are equal, $ p = -10 $ is the correct solution.

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Key Concepts

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

equation isolation

When solving a linear equation, our first goal often is to isolate the variable. This means we want to get the variable by itself on one side of the equation.

Let's look at the example given:

$$p + 8 = -2$$

Here, we need to isolate the variable 'p'. To do this, we need to remove the +8 on the left side of the equation. We do this by performing the opposite operation. Since we have +8, we need to subtract 8 on both sides:

\begin{align*} p + 8 - 8 & = -2 - 8 \ \ p & = -10 \end{align*}
By subtracting 8 from both sides, we have successfully isolated 'p' and found its value!

checking solutions

Once we find the solution to an equation, it鈥檚 important to check that our solution is correct.

In our example, we found that the solution is $ p = -10 $. To check this, we substitute $ -10 $ back into the original equation:

$$ -10 + 8 = -2 $$

On the left side, $ -10 + 8 $ simplifies to $ -2 $, which matches the right side of the equation. Since both sides of the equation are equal when $ p = -10 $, we can confidently say that our solution is correct.

Remember, this step is crucial because it verifies whether the solution truly satisfies the original equation or not.

prealgebra problems

Prealgebra often introduces students to the fundamentals of algebra, like solving simple linear equations. These types of problems help strengthen our understanding and skills for more complex algebra.

In the given problem, we deal with basic elements such as:

Variables (like 'p')
Constants (like 8 and -2)
Simple arithmetic operations (+ and -)

This forms a critical foundation. Once we master these simpler problems, we can progress to more complicated equations and concepts, feeling more prepared and confident in our mathematical abilities.

Practicing prealgebra problems ensures a solid understanding of how to manipulate equations and isolate variables, which will be pivotal throughout advanced math.

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91影视

In the following exercises, solve the equation. Then check your solution. $$ p+8=-2 $$

Short Answer

Step by step solution

- Isolate the variable

- Perform the operation

- Check the solution

Key Concepts

equation isolation

checking solutions

prealgebra problems

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