Answered

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Solve the inequality:
[tex]\[ |x+7| \ \textless \ 10 \][/tex]

Select one:
a. [tex]\(-3 \ \textless \ x \ \textless \ 10\)[/tex]
b. [tex]\(-10 \ \textless \ x \ \textless \ 3\)[/tex]
c. [tex]\(-17 \ \textless \ x \ \textless \ 3\)[/tex]
d. [tex]\(-13 \ \textless \ x \ \textless \ 10\)[/tex]

Sagot :

GinnyAnswer
To solve the inequality [tex]\( |x + 7| < 10 \)[/tex], we need to break it down into a less complex form. The expression [tex]\( |x + 7| < 10 \)[/tex] means that the distance between [tex]\( x + 7 \)[/tex] and 0 is less than 10. This condition can be translated into a compound inequality:

[tex]\[ -10 < x + 7 < 10 \][/tex]

Next, we solve for [tex]\( x \)[/tex] by isolating it in the middle of this inequality. To achieve this, we subtract 7 from all parts of the inequality:

[tex]\[ -10 - 7 < x + 7 - 7 < 10 - 7 \][/tex]

Simplifying the inequality:

[tex]\[ -17 < x < 3 \][/tex]

This gives us the range for [tex]\( x \)[/tex], which is:

[tex]\[ -17 < x < 3 \][/tex]

Thus, the correct answer is:

c. [tex]\( -17 < x < 3 \)[/tex]
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