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

Question

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

Answer 1

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].