https://file.aiquickdraw.com/mathbot/file/1729048414473ayp7gz8p.jpg

Let's solve the inequality:

\[
28 - 7x \leq -4(-7x - 7)
\]

### Step 1: Distribute the -4 on the right-hand side

Distribute the \(-4\) through the parentheses:

\[
28 - 7x \leq -4(-7x) - 4(-7)
\]
\[
28 - 7x \leq 28x + 28
\]

### Step 2: Move all terms involving \(x\) to one side

Add \(7x\) to both sides to collect the \(x\)-terms on the right-hand side:

\[
28 \leq 28x + 28 + 7x
\]
\[
28 \leq 35x + 28
\]

### Step 3: Subtract 28 from both sides

\[
28 - 28 \leq 35x
\]
\[
0 \leq 35x
\]

### Step 4: Solve for \(x\)

Now, divide both sides by 35:

\[
0 \leq x
\]
or equivalently:
\[
x \geq 0
\]

### Solution:

The solution to the inequality is:

\[
x \geq 0
\]

Would you like more details on any of these steps?

Here are some related questions for further exploration:
1. How can inequalities be solved graphically?
2. What happens to inequalities when multiplying or dividing by a negative number?
3. How do inequalities differ from equations in their solutions?
4. What are some real-world applications of inequalities?
5. How can compound inequalities be solved?

**Tip:** When solving inequalities, always reverse the inequality sign when multiplying or dividing both sides by a negative number.

Solve the inequality: 28 - 7x <= -4(-7x - 7)

Learn how to solve the inequality 28 - 7x <= -4(-7x - 7) with a detailed step-by-step solution, covering key algebraic concepts like the distributive property and solving linear inequalities. Ideal 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