how do you simplify
|4x + 8 - 10| ≥ 6 ?
because i got x ≤ 2 and x ≥ -6 as the answer.
But, someone else got x ≤ 2 and x ≥ -1..
(because they simplified by subtracting 8 to 10)
(it is absolute value)
so, i thought that you would add 10 to 6 to make |4x + 8| ≥ 6, but i noticed that some person subtracted 10 by 8 to make |4x + 2| ≥ 6 . So, i am wondering, how to simplify it?
|4x + 8 - 10| ≥ 6
|4x -2| ≥ 6
4x-2 ≥ 6 OR -4x+2 ≥ 6
4x ≥ 8 OR -4x ≥ 4
x ≥ 2 OR x ≤ -1
order of operation: the | ...| acts like a bracket, so you have to do inside the bracket first.
i have to simplify it to get it into the |ax + b| < c format, so that is why i must ask.
so you would subtract 8 by 10? not add 10 to 6?
To simplify the inequality |4x + 8 - 10| ≥ 6, we can break it down into two cases since the expression inside the absolute value can be positive or negative:
Case 1: 4x + 8 - 10 ≥ 6
In this case, we simplify the inequality as follows:
4x - 2 ≥ 6
Case 2: -(4x + 8 - 10) ≥ 6
In this case, we simplify the inequality as follows:
-4x - 8 + 10 ≥ 6
-4x + 2 ≥ 6
Now, let's solve each case separately:
Case 1:
4x - 2 ≥ 6
First, we add 2 to both sides to isolate the variable:
4x ≥ 8
Then, divide both sides by 4 to solve for x:
x ≥ 2
Case 2:
-4x + 2 ≥ 6
First, subtract 2 from both sides to isolate the variable:
-4x ≥ 4
Now, divide both sides by -4. However, since we are dividing by a negative number, the inequality sign must be flipped:
x ≤ -1
So, the solution to the inequality |4x + 8 - 10| ≥ 6 is x ≤ -1 or x ≥ 2.
It seems that you and the other person both made some mistakes in simplifying the expression inside the absolute value. In your case, you added 10 to 6 to make |4x + 8| ≥ 6, but that is incorrect. The expression inside the absolute value remains the same. On the other hand, the person who subtracted 10 from 8 made a mistake as well. The correct way to simplify it is to follow the steps I explained above.