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Solve the compound inequality for [tex]x[/tex]:
[tex]\[ 5 \leq x + 2 \leq 7 \][/tex]

Select one:
a. [tex]\[ 3 \leq x \leq 5 \][/tex]
b. [tex]\[ 7 \leq x \leq 9 \][/tex]
c. [tex]\[ 14 \leq x \leq 10 \][/tex]
d. [tex]\[ \frac{5}{2} \leq x \leq \frac{7}{2} \][/tex]

Sagot :

GinnyAnsweridn
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.
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