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Solve [tex]|x-4|+6=15[/tex].

A. [tex]x=-13[/tex] and [tex]x=5[/tex]
B. [tex]x=19[/tex] and [tex]x=-13[/tex]
C. [tex]x=13[/tex] and [tex]x=-5[/tex]
D. [tex]x=-13[/tex] and [tex]x=-5[/tex]

Sagot :

GinnyAnsweridn
To solve the equation [tex]\( |x-4| + 6 = 15 \)[/tex], follow these steps:

1. Isolate the Absolute Value:
Subtract 6 from both sides of the equation to isolate the absolute value term:
[tex]\[ |x-4| + 6 - 6 = 15 - 6 \][/tex]
[tex]\[ |x-4| = 9 \][/tex]

2. Consider the Definition of Absolute Value:
The equation [tex]\( |x-4| = 9 \)[/tex] means that [tex]\( x-4 \)[/tex] can be either 9 or -9. This gives us two separate equations to solve:
[tex]\[ x-4 = 9 \][/tex]
[tex]\[ x-4 = -9 \][/tex]

3. Solve Each Equation:
- For [tex]\( x-4 = 9 \)[/tex]:
[tex]\[ x = 9 + 4 \][/tex]
[tex]\[ x = 13 \][/tex]

- For [tex]\( x-4 = -9 \)[/tex]:
[tex]\[ x = -9 + 4 \][/tex]
[tex]\[ x = -5 \][/tex]

4. Conclusion:
The solutions to the equation [tex]\( |x-4| + 6 = 15 \)[/tex] are:
[tex]\[ x = 13 \quad \text{and} \quad x = -5 \][/tex]

Therefore, the correct answer is:

C. [tex]\( x = 13 \)[/tex] and [tex]\( x = -5 \)[/tex]
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