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]
