Solve the following inequality for zz. Write your answer in simplest form.

Question

minus, 6, minus, 2, left bracket, minus, 7, z, minus, 7, right bracket, is less than or equal to, z, minus, 1, minus, 10, z
−6−2(−7z−7)≤
z−1−10z

Answer 1

Starting with the left side of the inequality:

-6 - 2(-7z-7)
-6 + 14z + 14

Simplifying further:

8 + 14z

Now, considering the right side of the inequality:

z - 1 - 10z
-9z - 1

Putting it all together:

8 + 14z ≤ -9z - 1

To solve for zz, we can move all terms involving zz to one side of the inequality:

14z + 9z ≤ -1 - 8

Combining like terms:

23z ≤ -9

Dividing both sides by 23:

z ≤ -9/23

Therefore, the solution for zz is z ≤ -9/23.