https://file.aiquickdraw.com/mathbot/file/1726446613277arjllk7w.jpg

The inequality given in the image is:

\[
-12 > -4x + 20
\]

Let's solve this step by step.

### Step 1: Move the constant term to the other side
We want to isolate the \(x\)-term, so first subtract 20 from both sides:

\[
-12 - 20 > -4x
\]

Simplifying the left-hand side:

\[
-32 > -4x
\]

### Step 2: Solve for \(x\)
Now, divide both sides by \(-4\). When dividing by a negative number in an inequality, **the direction of the inequality must flip**:

\[
\frac{-32}{-4} < \frac{-4x}{-4}
\]

This simplifies to:

\[
8 < x
\]

or equivalently:

\[
x > 8
\]

### Final Answer:
The solution to the inequality is:

\[
x > 8
\]

Would you like more details on any step, or do you have any questions? 

Here are 5 related questions to expand your understanding:
1. What happens if we multiply or divide both sides of an inequality by a negative number?
2. How can you graph the solution \(x > 8\) on a number line?
3. How would the solution change if the inequality were \( -12 \geq -4x + 20 \)?
4. Can you provide an example of a similar inequality and solve it?
5. How would solving this inequality differ if the \(x\)-term had a positive coefficient?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number!

Learn how to solve the linear inequality -12 > -4x + 20 with a detailed step-by-step solution. This problem covers essential algebraic concepts, including solving inequalities and understanding how to handle negative coefficients. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation