Question

-19 less than -2x-5 or -2x-5 less than or equal to-23

Answer 1

-19 < -2x - 5 or -2x - 5 ≤ -23

To solve for x, we will solve each inequality separately:

-19 < -2x - 5

Add 5 to both sides:

-14 < -2x

Divide by -2 (and flip the inequality since we are dividing by a negative number):

7 > x

Now for the second inequality:

-2x - 5 ≤ -23

Add 5 to both sides:

-2x ≤ -18

Divide by -2 (and flip the inequality):

x ≥ 9

So, the two parts of the solution are:

x < 7 OR x ≥ 9

Alternatively, we can write the solution as the union of two intervals:

(-∞, 7) ∪ [9, +∞)