To solve the compound inequality [tex]\( 5 \leq x + 2 \leq 7 \)[/tex], we need to isolate [tex]\( x \)[/tex] in the middle of the inequality. Here is the step-by-step solution:
1. Write down the given compound inequality:
[tex]\[
5 \leq x + 2 \leq 7
\][/tex]
2. To isolate [tex]\( x \)[/tex], we need to get rid of the constant term [tex]\( +2 \)[/tex] by performing the same operation on all three parts of the inequality. Specifically, we subtract 2 from each part:
[tex]\[
5 - 2 \leq x + 2 - 2 \leq 7 - 2
\][/tex]
3. Simplify each part of the inequality:
[tex]\[
3 \leq x \leq 5
\][/tex]
The solution to the compound inequality [tex]\( 5 \leq x + 2 \leq 7 \)[/tex] is:
[tex]\[
3 \leq x \leq 5
\][/tex]
It corresponds to option a.
