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Recall that [tex]\(|x-1|\ \textless \ 5\)[/tex] can be written as [tex]\(-5\ \textless \ x-1\ \textless \ 5\)[/tex]. Which of the following represents the solutions of [tex]\(7 - |x-1|\ \textless \ 5\)[/tex]?

A. [tex]\(-2 \ \textless \ x \ \textless \ 8\)[/tex]
B. [tex]\(2 \ \textless \ x \ \textless \ 12\)[/tex]
C. [tex]\(-4 \ \textless \ x \ \textless \ 6\)[/tex]
D. [tex]\(1 \ \textless \ x \ \textless \ 11\)[/tex]



Answer :

GinnyAnswer
Let's solve the inequality step-by-step.

We start with the given inequality:
[tex]\[ |7 - (-1)| < 5 \][/tex]

First, simplify inside the absolute value:
[tex]\[ 7 - (-1) = 7 + 1 = 8 \][/tex]

Now we have:
[tex]\[ |8| < 5 \][/tex]

The absolute value of 8 is 8, so we are left with:
[tex]\[ 8 < 5 \][/tex]

Clearly, this statement is not true because 8 is greater than 5. Hence, there are no values of [tex]\( x \)[/tex] that satisfy the inequality.

Thus, the solution to the inequality [tex]\( |7 - (-1)| < 5 \)[/tex] is:
[tex]\[ \boxed{\text{There are no solutions.}} \][/tex]

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