braidenmorales1990
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Solve [tex]|x-5|=7[/tex]

A. [tex]x=-12[/tex] and [tex]x=-2[/tex]

B. [tex]x=12[/tex] and [tex]x=-12[/tex]

C. [tex]x=-12[/tex] and [tex]x=2[/tex]

D. [tex]x=12[/tex] and [tex]x=-2[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\(|x - 5| = 7\)[/tex], we need to consider that the absolute value expression has two possible scenarios. The absolute value equation [tex]\(|A| = B\)[/tex] translates into two equations: [tex]\(A = B\)[/tex] and [tex]\(A = -B\)[/tex].

Let's apply this principle to our given equation:

[tex]\[ |x - 5| = 7 \][/tex]

This can be broken down into two separate equations:

1. [tex]\(x - 5 = 7\)[/tex]
2. [tex]\(x - 5 = -7\)[/tex]

We will solve each equation individually:

### Solving the first equation:
[tex]\[ x - 5 = 7 \][/tex]

Add 5 to both sides to isolate [tex]\(x\)[/tex]:

[tex]\[ x = 7 + 5 \][/tex]

[tex]\[ x = 12 \][/tex]

### Solving the second equation:
[tex]\[ x - 5 = -7 \][/tex]

Add 5 to both sides to isolate [tex]\(x\)[/tex]:

[tex]\[ x = -7 + 5 \][/tex]

[tex]\[ x = -2 \][/tex]

Thus, the solutions to the equation [tex]\(|x - 5| = 7\)[/tex] are [tex]\(x = 12\)[/tex] and [tex]\(x = -2\)[/tex].

The correct answer is:

D. [tex]\(x = 12\)[/tex] and [tex]\(x = -2\)[/tex]
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