https://file.aiquickdraw.com/mathbot/file/17260891780194x7gfrnk.jpg

The inequality to solve is:

\[
5x - 12 \leq 3x - 4
\]

Let's solve it step by step:

### Step 1: Move all terms involving \(x\) to one side.
Subtract \(3x\) from both sides:

\[
5x - 3x - 12 \leq -4
\]

This simplifies to:

\[
2x - 12 \leq -4
\]

### Step 2: Move the constant terms to the other side.
Add 12 to both sides:

\[
2x \leq -4 + 12
\]

This simplifies to:

\[
2x \leq 8
\]

### Step 3: Solve for \(x\).
Divide both sides by 2:

\[
x \leq 4
\]

### Solution:
The solution is:

\[
x \leq 4
\]

### Graphing the solution:
On a number line, this inequality would be represented as a shaded region to the left of 4, including the point at \(x = 4\) (a closed circle at 4).

Would you like to go over any details of the solution? 

Here are some related questions:
1. How do you graph inequalities on a number line?
2. What is the difference between strict (\(<\)) and non-strict (\(\leq\)) inequalities in graphing?
3. How do you solve inequalities with variables on both sides?
4. What happens if you multiply or divide by a negative number when solving inequalities?
5. Can this inequality be written in interval notation?

**Tip**: When dividing or multiplying by a negative number in inequalities, don't forget to reverse the inequality sign!

Solve the inequality 5x - 12 ≤ 3x - 4 and graph the solution.

Learn how to solve the inequality 5x - 12 ≤ 3x - 4 step by step. This algebra problem covers key concepts like solving inequalities and graphing solutions. Ideal 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