To solve the compound inequality [tex]\( 5 \leq x+2 \leq 7 \)[/tex], we need to isolate the variable [tex]\( x \)[/tex]. Here are the steps to do that:
1. Start with the given compound inequality:
[tex]\[
5 \leq x+2 \leq 7
\][/tex]
2. To isolate [tex]\( x \)[/tex], we need to subtract 2 from each part of the inequality:
[tex]\[
5 - 2 \leq x + 2 - 2 \leq 7 - 2
\][/tex]
3. Simplifying each part, we get:
[tex]\[
3 \leq x \leq 5
\][/tex]
Thus, the solution to the compound inequality [tex]\( 5 \leq x+2 \leq 7 \)[/tex] is [tex]\( 3 \leq x \leq 5 \)[/tex].
Therefore, the correct choice is:
d. [tex]\( 3 \leq x \leq 5 \)[/tex]
