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

Question

Solve each inequality. Give the solution set in interval notation. 5| x + 1 | > 10

Accepted Answer

Hello everyone. We're going to solve the inequality nine times the absolute value of X plus two is greater than 81. So in this case we have a constant that is times are absolute value. Um And we need to take care of that before we work with the absolute value just like if the absolute value was parentheses so we have nine times X or nine times the absolute value of X plus two is greater than 81. I'm going to divide both sides by 9 to get that absolute value by itself. So now I have the absolute value of X plus two Is greater than nine. At this point we're gonna split this into two separate inequalities. We're gonna split it two. X plus two is greater than nine and X plus two is less than negative nine. We do this so we can hit all the possible values for X. So X plus two is greater than nine. I solved by subtracting two from both sides. I get the X has to be greater than seven is part of our solution but not the full thing and then X plus two is less than negative nine. I subtract two from both sides. I get X is less than negative 11. So when I think about these things in interval notation I know that I have X is greater than seven. So that means it starts at seven goes to positive infinity And I know I have X is less than -11. So that means it goes from -11 or sorry negative infinity to negative 11. So since these things go in opposite directions, we need to union them together. And when we do that we get the answer choice of C. So it is the union of negative infinity to negative 11 and seven to positive infinity. Have a nice day.

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Solve each inequality. Give the solution set in interval notation. 5| x + 1 | > 10