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Chapter 3: Problem 33

Solve the equation. $$12 p=3 p+36$$

Short Answer

Expert verified
p = 4

Step by step solution

01

- Combine Like Terms

First, subtract \(3p\) from both sides of the equation to combine like terms on one side. The equation is: \(12p - 3p = 36\).
02

- Simplify the Equation

Simplify the left-hand side by performing the subtraction: \(9p = 36\).
03

- Solve for p

To isolate \(p\), divide both sides of the equation by 9: \(p = \frac{36}{9}\).
04

- Simplify the Fraction

Simplify the fraction \(\frac{36}{9}\): \(p = 4\).

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Key Concepts

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

combining like terms
Combining like terms is an important step in solving linear equations. Terms are considered 'like terms' if they have the same variable raised to the same power.
In the equation given, we have the terms \(12p\) and \(3p\).
Both of these terms have the variable \(p\), making them like terms.

First, subtract \(3p\) from both sides to move all terms with \(p\) to one side:
\(12p - 3p = 36\). This simplifies the equation to:
\(9p = 36\).

Combining like terms helps in making the equation simpler and easier to solve.
isolating the variable
Isolating the variable is key to finding the solution of the equation. Isolating means getting the variable on its own on one side of the equation.
From the simplified equation \(9p = 36\), our goal is to have \(p\) alone.
To isolate \(p\), we divide both sides by 9:
\(p = \frac{36}{9}\).

This step is crucial because it targets the variable directly, making it easier to compute its value.
simplifying fractions
Simplifying fractions brings clarity and simplicity to the final answer. Once we have isolated the variable, we need to simplify the fraction.

In the current equation, we have:
\(p = \frac{36}{9}\).
By simplifying \(\frac{36}{9}\), we get:
\(p = 4\).

Always look for the greatest common divisor (GCD) to simplify fractions efficiently. Here, 9 is the GCD of both 36 and 9.

By simplifying fractions, we ensure that the result is in its simplest form, making it easier to interpret and use.

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Most popular questions from this chapter

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