Solve the following inequality for vv. Write your answer in simplest form.
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
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.
To solve the inequality, let's simplify the expressions first:
9v - (6v + 3) ≤ -6v - 8 + 4
Distribute the negative sign to the terms inside the parentheses:
9v - 6v - 3 ≤ -6v - 8 + 4
Combine like terms:
3v - 3 ≤ -6v - 4
Add 6v to both sides of the inequality to get the variable terms on one side:
3v + 6v - 3 ≤ -4
Combine like terms again:
9v - 3 ≤ -4
Add 3 to both sides of the inequality to isolate the variable:
9v - 3 + 3 ≤ -4 + 3
Simplify:
9v ≤ -1
Divide both sides of the inequality by 9 to solve for v:
9v/9 ≤ -1/9
Simplify:
v ≤ -1/9
Therefore, the solution to the inequality is v ≤ -1/9.
To solve the inequality, we can follow a few steps:
Step 1: Simplify both sides of the inequality by removing the brackets.
9v - (6v + 3) ≤ -6v - 8 + 4
Step 2: Distribute the negative sign to simplify the left side.
9v - 6v - 3 ≤ -6v - 8 + 4
3v - 3 ≤ -6v - 4
Step 3: Collect like terms on the left side and right side separately.
3v + 6v ≤ -4 + 3
9v ≤ -1
Step 4: Divide both sides of the inequality by 9 to isolate the variable.
(9v)/9 ≤ -1/9
v ≤ -1/9
So, the solution to the inequality is v ≤ -1/9.