2<−2x+6or

Question

−18>−2x+6

Answer 1

To solve the inequality 2 < -2x + 6, we need to isolate the variable x.

First, subtract 6 from both sides:
2 - 6 < -2x + 6 - 6
-4 < -2x

Next, divide both sides by -2. Remember, when dividing by a negative number, we need to flip the inequality sign:
-4 / -2 > -2x / -2
2 > x

So, the solution to the inequality 2 < -2x + 6 is x < 2.

Now, let's solve the inequality -18 > -2x + 6:
-18 - 6 > -2x
-24 > -2x

Dividing both sides by -2 (and flipping the inequality sign):
-24 / -2 < -2x / -2
12 < x

So, the solution to the inequality -18 > -2x + 6 is x > 12.

In summary, the solutions to the two inequalities are:
2 < x < 12