Solve the following inequality for zz. Write your answer in simplest form.
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
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.
To solve the inequality, let's simplify both sides step-by-step:
Starting with the left side:
-6 - 2(-7z - 7)
-6 + 14z + 14
Simplifying further:
14z + 8
Now let's simplify the right side:
z - 1 - 10z
-9z - 1
Now we have:
14z + 8 ≤ -9z - 1
To isolate the variable z, let's add 9z to both sides:
14z + 9z + 8 ≤ -1
Combining like terms:
23z + 8 ≤ -1
Next, subtract 8 from both sides:
23z ≤ -9
Lastly, divide both sides by 23:
z ≤ -9/23
So the solution to the inequality is z ≤ -9/23.
To solve the inequality, let's simplify the expression on both sides first.
Starting with the left side:
-6 - 2(-7z - 7)
Simplify by distributing the -2 to both terms inside the parentheses:
-6 + 14z + 14
Combine like terms:
14z + 8
Now let's simplify the right side:
z - 1 - 10z
Combine like terms:
-9z - 1
So, the inequality becomes:
14z + 8 ≤ -9z - 1
To solve this inequality for z, let's isolate the variable on one side of the inequality sign.
Add 9z to both sides:
14z + 9z + 8 ≤ -1
Combine like terms:
23z + 8 ≤ -1
Next, subtract 8 from both sides:
23z ≤ -9
Finally, divide both sides by 23 to solve for z:
z ≤ -9/23
Therefore, the solution to the inequality is:
z ≤ -9/23