https://file.aiquickdraw.com/mathbot/file/1728673231141j3evpmrb.jpg

The inequality in the image is:

\[
-2(v + 2) + 22 < 4(7 - v)
\]

Let's solve this step-by-step:

### Step 1: Distribute the terms.
Distribute the \(-2\) on the left-hand side and the \(4\) on the right-hand side:

\[
-2v - 4 + 22 < 28 - 4v
\]

### Step 2: Combine like terms.
On the left-hand side:

\[
-2v + 18 < 28 - 4v
\]

### Step 3: Add \(4v\) to both sides to move the variable terms to one side:

\[
-2v + 4v + 18 < 28
\]

\[
2v + 18 < 28
\]

### Step 4: Subtract 18 from both sides:

\[
2v < 28 - 18
\]

\[
2v < 10
\]

### Step 5: Divide both sides by 2:

\[
v < 5
\]

### Final solution:
\[
v < 5
\]

The solution to the inequality is \(v < 5\).

Do you have any questions, or would you like more details on any of the steps?

Here are 5 follow-up questions:
1. How do you graph the solution \(v < 5\) on a number line?
2. What changes if the inequality sign was \( \leq \) instead of \( < \)?
3. How would you solve the inequality if there was a negative variable coefficient, like \(-4v\)?
4. Can you solve an inequality where both sides contain fractions?
5. How do you check if a solution to an inequality is correct?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number flips the inequality sign!

Learn how to solve the inequality -2(v + 2) + 22 < 4(7 - v) with step-by-step explanations. This problem involves key algebraic concepts such as the distributive property and inequality rules. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation