Solve the following inequality for ff. Write your answer in simplest form.
8, plus, 4, left parenthesis, minus, f, minus, 6, right parenthesis, is less than or equal to, 4, f, minus, 6, minus, 2, f
8+4(−f−6)≤
4f−6−2f

Let's solve the inequality step by step:

The given inequality is:

\[
8 + 4(-f - 6) \leq 4f - 6 - 2f
\]

### Step 1: Distribute the 4 on the left-hand side.

\[
8 + 4(-f) + 4(-6) \leq 4f - 6 - 2f
\]

Simplifying:

\[
8 - 4f - 24 \leq 4f - 6 - 2f
\]

### Step 2: Combine like terms on both sides.

On the left-hand side:

\[
8 - 24 = -16
\]

So, the inequality becomes:

\[
-16 - 4f \leq 4f - 6 - 2f
\]

On the right-hand side, combine \(4f\) and \(-2f\):

\[
4f - 2f = 2f
\]

Now, the inequality is:

\[
-16 - 4f \leq 2f - 6
\]

### Step 3: Move all terms involving \(f\) to one side and constant terms to the other side.

Add \(4f\) to both sides:

\[
-16 \leq 2f + 4f - 6
\]

Simplifying:

\[
-16 \leq 6f - 6
\]

### Step 4: Isolate \(f\).

Add 6 to both sides:

\[
-16 + 6 \leq 6f
\]

Simplifying:

\[
-10 \leq 6f
\]

### Step 5: Solve for \(f\).

Divide both sides by 6:

\[
\frac{-10}{6} \leq f
\]

Simplify the fraction:

\[
\frac{-5}{3} \leq f
\]

This can also be written as:

\[
f \geq \frac{-5}{3}
\]

### Final Answer:
\[
f \geq \frac{-5}{3}
\]

Let me know if you need more details or have any questions!

---

Here are 5 related questions:
1. How do we solve multi-step inequalities in general?
2. What happens if we multiply or divide both sides of an inequality by a negative number?
3. Can you explain the importance of distributing correctly in inequalities?
4. How do we graph inequalities on a number line?
5. What are the steps to combine like terms in inequalities?

**Tip:** Always check your solution by substituting it back into the original inequality to ensure it satisfies the condition.

Solve the following inequality for f: 8 + 4(-f - 6) ≤ 4f - 6 - 2f

Step-by-step solution for solving the inequality 8 + 4(-f - 6) ≤ 4f - 6 - 2f. Learn how to apply the distributive property, combine like terms, and solve for f in algebraic inequalities. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation