Solve each equation or inequality. | 5x + 1/2 | -2

Question

Solve each equation or inequality. | 5x + 1/2 | -2 < 5

Accepted Answer

Hello everyone. We're going to find the solution set for the absolute value inequality. The absolute value of 11 X plus 3/4 minus four Is less than 16. First thing I recognize is that I do have an absolute value but I also have a -4 that is not within the absolute value. So I want to get rid of that first. I'm going to do this by adding affordable sides. So now I'm left with the absolute value of 11 X plus 33 4th Is less than 20. Now I recall that I need to split up my absolute value inequality into two separate inequalities. So I'm gonna have 11 X plus 3/ Is less than 20. I also need to do the opposite so I need to do 11 X plus 3/4 is greater than negative 20. And once I do both of those I will have my full solution set. So starting with 11 x plus 3/4 is less than I'm gonna solve by subtracting 3/4 from both sides. Um So I get 11 X. Is less than 77 4th Divide both sides by 11. Um recalling that, dividing a fraction is multiplied by its reciprocal. That's like multiplying by 1/11. So I'm gonna cross reduce those 11 with 77 And I get that X. is less than 7/4 which in interval notation would be negative infinity. 2/7/4 with a parentheses this is gonna be part of our solution. Not quite done yet. On the other side I have 11 X plus 3/4 is greater than negative 20. Again, I'm gonna start by subtracting 3/4 from both sides. So this gives me 11 x is greater than -83/4. Again, I'm gonna divide both sides by 11, which is the same as multiplying by the reciprocal, which is 1/11. So I get X is greater than -83/44, which in interval notation would be negative 83/44 with a parentheses next to it to positive infinity. So these are two solutions and now we need to look at them and see if there's overlap or if we need to use the union of them. So since negative 83/44 is less than 7/4, our solution is actually going to be the overlap. So it's gonna be all of the values that are greater than -83/44 but are less than 7/ and that looks like it is answer choice B have a next day

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Solve each equation or inequality. | 5x + 1/2 | -2 < 5

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