Get the most out of your questions with the extensive resources available on IDNLearn.com. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.

Select the correct answer.

How many solutions for [tex]$x$[/tex] does the following equation have?

[tex]$2(x+4) - 1 = 2x + 7$[/tex]

A. 1
B. 7
C. Infinite
D. 0


Sagot :

To determine the number of solutions for the equation [tex]\(2(x + 4) - 1 = 2x + 7\)[/tex], let's go through the steps.

1. Distribute the 2 inside the parentheses:
[tex]\[ 2(x + 4) - 1 = 2x + 7 \][/tex]
This becomes:
[tex]\[ 2x + 8 - 1 = 2x + 7 \][/tex]

2. Simplify the left side:
[tex]\[ 2x + 7 = 2x + 7 \][/tex]

3. Subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[ 2x + 7 - 2x = 2x + 7 - 2x \][/tex]
This results in:
[tex]\[ 7 = 7 \][/tex]

At this point, we observe that the equation [tex]\(7 = 7\)[/tex] is always true, regardless of the value of [tex]\(x\)[/tex]. This indicates that the original equation is an identity and holds for all possible values of [tex]\(x\)[/tex].

Therefore, the equation [tex]\(2(x + 4) - 1 = 2x + 7\)[/tex] does not have a specific, finite number of solutions but rather has an infinite number of solutions.

Thus, the correct answer is:
C. infinite