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

Question

9, v, minus, left bracket, 6, v, plus, 3, right bracket, is less than or equal to, minus, 6, v, minus, 8, plus, 4
9v−(6v+3)≤
−6v−8+4

Answer 1

To solve the inequality, we first simplify both sides:

On the left side, we distribute the negative sign:
9v - (6v + 3) = 9v - 6v - 3 = 3v - 3.

On the right side, we combine like terms:
-6v - 8 + 4 = -6v - 4.

So the inequality becomes:
3v - 3 ≤ -6v - 4.

Next, we want to isolate the v term on one side of the inequality. We can do this by adding 6v to both sides:
3v - 3 + 6v ≤ -6v - 4 + 6v. Simplifying this gives us:
9v - 3 ≤ -4.

Finally, we add 3 to both sides to isolate the v term:
9v - 3 + 3 ≤ -4 + 3. Simplifying this gives us:
9v ≤ -1.

To find the value of v, we can divide both sides by 9:
(9v)/9 ≤ (-1)/9. Simplifying this gives us:
v ≤ -1/9.

So the solution to the inequality is v ≤ -1/9.