Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Consider the equation [tex]3p - 7 + p = 13[/tex]. What is the resulting equation after the first step in the solution?

A. [tex]p - 7 = 13 - 3p[/tex]
B. [tex]2p - 7 = 13[/tex]
C. [tex]3p - 7 = 13 - p[/tex]
D. [tex]4p - 7 = 13[/tex]

Sagot :

GinnyAnswer
Let's take a detailed, step-by-step approach to solve the equation and determine the correct answer:

1. Given Equation:
[tex]\[ 3p - 7 + p = 13 \][/tex]

2. Combine Like Terms:
Combine the [tex]\( p \)[/tex] terms on the left side.
[tex]\[ 3p + p - 7 = 13 \][/tex]
Simplify by adding the coefficients of [tex]\( p \)[/tex]:
[tex]\[ 4p - 7 = 13 \][/tex]

3. Isolate [tex]\( 4p \)[/tex]:
To get [tex]\( 4p \)[/tex] by itself, move the constant term [tex]\(-7\)[/tex] to the right side of the equation.
Add [tex]\( 7 \)[/tex] to both sides:
[tex]\[ 4p - 7 + 7 = 13 + 7 \][/tex]
This simplifies to:
[tex]\[ 4p = 20 \][/tex]

The initial step to isolate [tex]\( 4p \)[/tex] was done here:
When the constants are moved and terms are simplified, one of the intermediate steps would be noticing that the equation transformed and simplified, as shown here:

So the resulting equation after the first step in the solution is:
[tex]\[ 4p - 7 = 13 \][/tex]

Thus, the correct answer is:
[tex]\[ 4p - 7 = 13 \][/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.