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Chapter 8: Problem 9

In the following exercises, solve each equation. $$ p+2.4=-9.3 $$

Short Answer

Expert verified
p = -11.7

Step by step solution

01

- Isolate the Variable

To isolate the variable ( p ), subtract 2.4 from both sides of the equation. p + 2.4 - 2.4 = -9.3 - 2.4
02

- Simplify Both Sides

Simplify the left and right sides of the equation. p = -9.3 - 2.4 Calculate the value.
03

- Calculate the Right Side

Perform the subtraction on the right side of the equation. -9.3 - 2.4 = -11.7 Thus, p = -11.7

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Key Concepts

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

Variable Isolation
In solving linear equations, the first important step is variable isolation. Our goal is to get the variable (in this case, p) by itself on one side of the equation.

To isolate a variable, we need to move all other terms to the opposite side of the equation. We use the opposite operation (addition becomes subtraction and vice versa) to do this.

In the example given, we start with the equation:

p + 2.4 = -9.3

To isolate the variable p, we subtract 2.4 from both sides:

p + 2.4 - 2.4 = -9.3 - 2.4

Notice how subtracting 2.4 cancels out the +2.4 on the left side, leaving just p on that side:


p = -9.3 - 2.4

This key step clarifies the need to perform the same operation on both sides of the equation to maintain balance.

Simplifying Equations
Simplifying an equation makes it easier to solve. Once we've isolated the variable, the next step is to simplify both sides. Let's recap from the previous step:


p = -9.3 - 2.4

Here, simplifying means performing the arithmetic operations needed to clear the values on the right side of the equation. Simplification process involves:
  • Combining like terms
  • Performing any arithmetic operations such as addition, subtraction, multiplication, or division

In this example, we need to subtract 2.4 from -9.3:

-9.3 - 2.4

Combining these we get:


p = -11.7

Thus, the simplified equation provides us with the value of p. This step highlights the importance of performing operations correctly to avoid mistakes and achieve the correct solution.
Basic Arithmetic Operations
Performing basic arithmetic operations is fundamental in solving equations. Here, we handle operations like addition, subtraction, multiplication, and division.

In the provided exercise, we focus on subtraction. We need to subtract 2.4 from -9.3:

-9.3 - 2.4

To accomplish this, we follow standard arithmetic rules. First, we note that both numbers are negative, so we add their absolute values and then place the negative sign back in the result:

|-9.3| + |2.4| = 9.3 + 2.4 = 11.7

Then, we apply the negative sign back:

-11.7

This gives us our result:


p = -11.7

Mastery of basic arithmetic operations ensures accuracy in solving more complex equations, making each step reliable and understandable.

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