Find the solution of the following inequality 12x+31_< 5

To solve the inequality:

\[
12x + 31 \leq 5
\]

### Step-by-Step Solution:

1. **Isolate the term with \(x\):**
   Subtract 31 from both sides:

   \[
   12x \leq 5 - 31
   \]

   Simplify the right side:

   \[
   12x \leq -26
   \]

2. **Solve for \(x\):**
   Divide both sides by 12:

   \[
   x \leq \frac{-26}{12}
   \]

   Simplify the fraction:

   \[
   x \leq -\frac{13}{6}
   \]

### Final Answer:

The solution to the inequality is:

\[
x \leq -\frac{13}{6}
\]

### Additional Questions:

1. What is the decimal representation of \(-\frac{13}{6}\)?
2. How would the solution change if the inequality were \(12x + 31 > 5\)?
3. How do you graph the solution set \(x \leq -\frac{13}{6}\) on a number line?
4. What are the possible integer values of \(x\) that satisfy the inequality?
5. How would you solve the inequality if it were \(12x + 31 \geq 5\)?

### Tip:

When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number!

Find the solution of the following inequality 12x + 31 <= 5

Learn how to solve the linear inequality 12x + 31 <= 5 with a clear, step-by-step guide. This solution covers important algebraic concepts, including isolating terms and dividing inequalities. 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