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Try to rewrite this inequality as a compound inequality.
Solution Set: {y | y≤- 54 or y≥ 94}
Graph:
We are asked to find and graph the solution set for all possible values of y in the given inequality. Let's begin by isolating the absolute value in the inequality.
6|4y-2|≥ 42 ⇒ |4y-2|≥ 7
Now, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between 4y and 2 greater than or equal to 7 in the positive direction or in the negative direction.
4y-2 ≥ 7 or 4y-2≤ -7
We are now going to solve the first inequality.
This inequality tells us that all values greater than or equal to 94 will satisfy the inequality.
Let's now move on to the second inequality.
This inequality tells us that all values less than or equal to - 54 will satisfy the inequality.
The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& y≥ 94 Second Solution Set:& y≤ - 54 Combined Solution Set:& y≤ - 54 or y≥ 94
The graph of this inequality includes all values less than or equal to - 54 or greater than or equal to 94. We show this by keeping the endpoints closed.
