https://file.aiquickdraw.com/mathbot/file/17267914878417w127jqt.jpg

Let's solve the inequality step by step:

The given inequality is:
\[
-2(x - 7) \geq 3x - 11
\]

### Step 1: Expand the left-hand side
Distribute the \(-2\) on the left-hand side:

\[
-2(x - 7) = -2x + 14
\]

So the inequality becomes:
\[
-2x + 14 \geq 3x - 11
\]

### Step 2: Move terms involving \(x\) to one side
Add \(2x\) to both sides to get rid of the \(-2x\) on the left side:

\[
14 \geq 5x - 11
\]

### Step 3: Move constant terms to the other side
Add \(11\) to both sides to isolate the term with \(x\) on the right side:

\[
25 \geq 5x
\]

### Step 4: Solve for \(x\)
Now, divide both sides by 5 to solve for \(x\):

\[
5 \geq x
\]

or equivalently:
\[
x \leq 5
\]

### Final Solution:
The solution to the inequality is:
\[
x \leq 5
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve inequalities with fractions?
2. What changes when you multiply or divide both sides of an inequality by a negative number?
3. Can you solve a quadratic inequality?
4. How do you represent the solution to an inequality on a number line?
5. What are compound inequalities, and how do you solve them?

**Tip:** When solving inequalities, remember that flipping the inequality sign occurs only when multiplying or dividing both sides by a negative number.

Find the solution set for the inequality: -2(x - 7) ≥ 3x - 11

Learn how to solve the linear inequality -2(x - 7) ≥ 3x - 11 with step-by-step instructions. This problem covers key algebraic concepts, including the distributive property and properties of 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