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Which number line represents the solutions to [tex]|x-2|=6[/tex]?

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GinnyAnsweridn
To solve the equation [tex]\( |x - 2| = 6 \)[/tex], we need to consider the definition of absolute value. The absolute value equation [tex]\( |a| = b \)[/tex] implies two possible equations: [tex]\( a = b \)[/tex] or [tex]\( a = -b \)[/tex].

So, for the equation [tex]\( |x - 2| = 6 \)[/tex]:

1. We set [tex]\( x - 2 \)[/tex] equal to 6:
[tex]\[ x - 2 = 6 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 6 + 2 \][/tex]
[tex]\[ x = 8 \][/tex]

2. We set [tex]\( x - 2 \)[/tex] equal to -6:
[tex]\[ x - 2 = -6 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = -6 + 2 \][/tex]
[tex]\[ x = -4 \][/tex]

Thus, the solutions to the equation [tex]\( |x - 2| = 6 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -4 \)[/tex].

To represent these solutions on the number line:

1. Draw a horizontal line and mark important points, particularly [tex]\( -4 \)[/tex] and [tex]\( 8 \)[/tex].

2. Place a point at [tex]\( -4 \)[/tex] and a point at [tex]\( 8 \)[/tex].

These two points, [tex]\( -4 \)[/tex] and [tex]\( 8 \)[/tex], are the solutions to the equation [tex]\( |x - 2| = 6 \)[/tex].
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