Solve each inequality. Give the solution set in interval notation...

Question

Solve each inequality. Give the solution set in interval notation. | 7 - 3x | > 4

Accepted Answer

Hello everyone. We're going to solve the inequality. The absolute value of one minus two X. Is greater than 37. Recall that when we're solving an absolute value we have two different inequalities. So we will have one minus two X. Is greater than 37. But we also need to solve 1 -2 X is less than -37. This will give us all of our possibilities for our x value. And when we're done we're going to put it in interval notation. So for 1 -2 x is greater than 37. 1st thing I'm gonna do is subtract one from both sides. You get -2. X is greater than 36. To get the X by itself. I divide both sides by -2. Recall that when we divide an inequality by a negative we have to flip our inequality symbol. So now I have X is less than -18. What that looks like an interval notation is that it goes from negative infinity to negative 18. So this is half of our solution. It's not done just yet. We still need to do 1 -2. X is less than -37. So I'm gonna start out the same way by subtracting one from both sides. So I have negative two. X is less than negative, 38, Dividing both sides by -2. You get X by itself on the left side. And again remember to flip the inequality so I have X is greater than And -38 divided by two is positive 19. So what that looks like an interval notation? It would go from 19 to positive infinity. So now looking at them, is there an overlap? There is not because negative infinity to negative 18 has no overlap with 19 to positive infinity. So we need the union of those two sections and that is going to give us answer choice C negative infinity to negative 18. Union 19 to positive infinity. Have a nice day.

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Solve each inequality. Give the solution set in interval notation. | 7 - 3x | > 4

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