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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 :

GinnyAnswer
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
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