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Chapter 3: Problem 42

Solve the equation. $$6 p=-18$$

Short Answer

Expert verified
p = -3

Step by step solution

01

- Identify the equation

The given equation is: \[6p = -18\]
02

- Isolate the variable

To solve for \(p\), divide both sides of the equation by 6:\[ \frac{6p}{6} = \frac{-18}{6}\]
03

- Simplify both sides

Simplify the fractions to isolate \(p\):\[ p = -3 \]

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Key Concepts

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

Equation Solving
Solving equations is a core skill in algebra. In simple terms, solving an equation means finding the value of the variable that makes the equation true.
For instance, in the equation \(6p = -18\), solving it means figuring out what value of \p\ will make both sides equal. Here's a friendly step-by-step approach:
鈥� First, identify the equation.
鈥� Then, manipulate the equation to isolate the variable.
鈥� Finally, simplify to get the final value of the variable.
In our example, \(p = -3\) is the solution because when you substitute \p\ with \ -3\, both sides of the equation balance perfectly.
Isolating Variables
Isolating variables is crucial in solving equations. To isolate a variable means to get it by itself on one side of the equation.
This process involves several steps:
  • Perform operations that simplify the equation.
  • Use inverse operations to move terms involving the variable to one side and constants to the other.
  • Divide or multiply to solve for the variable.
The goal is to simplify the appearance and leave the variable alone.
In the equation \(6p = -18\), we isolated \p\ by dividing both sides by 6. This gave us \( \frac{6p}{6} = \frac{-18}{6} \), simplifying further to \p = -3\.
Simplification
Simplification in algebra involves reducing an equation or expression to its simplest form.
This often means combining like terms, canceling out common factors, or performing basic arithmetic operations.
In the equation-solving example \(6p = -18\), we simplified \( \frac{6p}{6} = \frac{-18}{6} \) by performing division. This simplified both sides to get \p = -3\.
Remember, simplification makes equations easier to handle and understand.
Prealgebra
Prealgebra forms the foundation for all higher-level math. It introduces basic concepts like variables, simple equations, and fundamental operations.
When dealing with linear equations, prealgebra skills are essential.
Consider the example \(6p = -18\):
  • You start with understanding what the equation represents.
  • Next, you use basic operations to isolate and solve for the variable.
Mastering these skills early on sets you up for success in algebra and beyond.

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