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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]
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