How do you solve this inequality 2 ≤ 4 - ½x

Question

How do you solve this inequality 2 ≤ 4 - ½x < 7

oaktree · Answer

OK. These are pretty simple - just solve it like you would a normal inequality, except whatever you do, do it to both sides. So just work on isolating the x.

jdoe0001 · Answer

$\bf 2 \le 4 -\cfrac{1}{2}x < 7\
 -2 \le -\cfrac{1}{2}x < 3$

as OakTree  already pointed out, we substracted "4" from ALL 3 sides
left, middle, right
so we go isolating "x" to solve for "x"
now the next step will be to multiply by a number that gets rid of the -1/2 in the middle, so we isolate the "x"

jdoe0001 · Answer

so to get rid of the -1/2, we can just multiply by $\bf \text{-2}$ :)

now, keep in mind that in inequalities, whenever you multiply, divide or exponentialize by a negative number, you have to $\bf \text{flip the sign}$