Find a statement that is equivalent to the absolute value inequality

Answer:

Option 5: -4 ≤ 7x - 7 ≤ 4

Step-by-step explanation:

It is required to find which expression is equivalent to |7x-7| ≤ 4

So, at the beginning we should review the rules of absolute value inequalities.

1) If |x| ≤ a ⇒ -a ≤ x ≤ a

2) If |x| < a ⇒ -a < x < a

3) If |x| ≥ a ⇒ x ≤ -a or x  ≥  a

4) If |x| > a ⇒ x < -a or x  >  a

Applying the first rule to the given absolute value inequality:

|7x-7| ≤ 4  ⇒  -4 ≤ 7x-7 ≤ 4

So, the answer is option 5

its the fourth option

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