Solve the following inequality for ff. Write your answer in simplest form.
8, minus, left bracket, minus, 4, f, minus, 3, right bracket, is less than or equal to, minus, f, minus, 8, plus, 2, f
8−(−4f−3)≤
−f−8+2f
Simplifying the left side of the inequality:
8 - (-4f - 3) = 8 + 4f + 3 = 11 + 4f
Simplifying the right side of the inequality:
-f - 8 + 2f = f - 8
Now, the inequality becomes:
11 + 4f ≤ f - 8
Subtracting 4f from both sides:
11 ≤ -3f - 8
Adding 8 to both sides:
19 ≤ -3f
Dividing by -3 and flipping the inequality sign:
-6.33... ≥ f
So, the solution to the inequality is f ≤ -6.33, or in interval notation: (-∞, -6.33].
To solve this inequality, follow these steps:
Step 1: Simplify both sides of the equation.
On the left side, distribute the negative sign inside the bracket:
8 + 4f + 3 ≤ -f - 8 + 2f
Simplify the equation:
8 + 4f + 3 ≤ -f - 8 + 2f
8 + 7f + 3 ≤ -8 + f
Combine like terms:
11 + 7f ≤ -8 + f
Step 2: Isolate the variable on one side of the inequality.
To get all the f terms on one side and the constants on the other side, subtract f from both sides and subtract 11 from both sides:
7f - f ≤ -8 - 11
6f ≤ -19
Step 3: Solve for the variable.
To solve for f, divide both sides of the equation by 6:
(6f)/6 ≤ (-19)/6
f ≤ -19/6
Therefore, the solution to the inequality is f ≤ -19/6.
To solve the given inequality, we can use the steps below:
Step 1: Simplify both sides of the inequality:
On the left side, we can simplify the expression within the brackets:
8 - (-4f - 3) = 8 + 4f + 3 = 11 + 4f
On the right side, combine the like terms:
-f - 8 + 2f = f - 8
The inequality becomes:
11 + 4f ≤ f - 8
Step 2: Isolate the variable on one side of the inequality:
To isolate the variable "f" on the left side, we need to move the term "4f" to the right side. We can do this by subtracting 4f from both sides of the inequality:
11 + 4f - 4f ≤ f - 8 - 4f
Simplifying this further:
11 ≤ -3f - 8
Step 3: Continue isolating the variable:
Next, we want to move the constant terms to the right side of the inequality. We can do this by adding 8 to both sides:
11 + 8 ≤ -3f - 8 + 8
Simplifying:
19 ≤ -3f
Step 4: Divide both sides by the coefficient of "f" to solve for "f":
To isolate "f", divide both sides by -3, but since we are dividing by a negative number, the direction of the inequality flips:
19 / -3 ≥ -3f / -3
Simplifying:
-19/3 ≥ f
Step 5: Simplify the answer:
The given inequality, in simplest form, is:
f ≤ -19/3