Question

What is the inequality??? 9x-13<-22 or -8x+7≤-25

Answer 1

awnser picture below

Answer 2

x<−1 and

�

≥

4

x≥4.

Explanation:

9x−13<−22

−

8

�

+

7

≤

−

25

−8x+7≤−25

Let's solve each of these inequalities separately:

9

�

−

13

<

−

22

9x−13<−22

Add 13 to both sides:

9

�

−

13

+

13

<

−

22

+

13

9x−13+13<−22+13

This simplifies to:

9

�

<

−

9

9x<−9

Now, divide both sides by 9:

9

�

9

<

−

9

9

9

9x

​

<

9

−9

​

�

<

−

1

x<−1

So the solution to the first inequality is

�

<

−

1

x<−1.

−

8

�

+

7

≤

−

25

−8x+7≤−25

Subtract 7 from both sides:

−

8

�

+

7

−

7

≤

−

25

−

7

−8x+7−7≤−25−7

Simplify:

−

8

�

≤

−

32

−8x≤−32

Now, divide both sides by -8, and remember to reverse the inequality sign when dividing by a negative number:

−

8

�

−

8

≥

−

32

−

8

−8

−8x

​

≥

−8

−32

​

�

≥

4

x≥4

So the solution to the second inequality is

�

≥

4

x≥4.

Therefore, the solutions to the system of inequalities are

�

<

−

1

x<−1 and

�

≥

4

x≥4.