Question

question 9 of 34 step 1 of 2
consider the following absolute value inequality.
|-6y + 7| ≥ 37
step 1 of 2: rewrite the given inequality as two linear inequalities.
enter the two inequalities in the boxes and select the proper word to join the inequalities.
inequalities:
and
or

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| \geq B\) (where \(B>0\)), it is equivalent to \(A \geq B\) or \(A \leq -B\). Here, \(A=-6y + 7\) and \(B = 37\).

Step2: Apply the rule to the given inequality

Using the rule, we get two inequalities: \(-6y + 7 \geq 37\) and \(-6y + 7 \leq - 37\). And the word to join them is "or" because the absolute value being greater than or equal to a number means the expression inside is either greater than or equal to that number or less than or equal to the negative of that number.

Answer:

First inequality: \(-6y + 7 \geq 37\), Second inequality: \(-6y + 7 \leq -37\), Join with: or