To solve the inequality \( 8x + 4 < 12x - 100 \), follow these steps:

1. Subtract \( 8x \) from both sides to start isolating the variable \( x \):
   \[
   8x + 4 - 8x < 12x - 100 - 8x
   \]
   Simplifying, you get:
   \[
   4 < 4x - 100
   \]

2. Add 100 to both sides to further isolate the term with \( x \):
   \[
   4 + 100 < 4x - 100 + 100
   \]
   Simplifying, you get:
   \[
   104 < 4x
   \]

3. Divide both sides by 4 to solve for \( x \):
   \[
   \frac{104}{4} < \frac{4x}{4}
   \]
   Simplifying, you get:
   \[
   26 < x
   \]
   This can also be written as:
   \[
   x > 26
   \]

The solution to the inequality is:
\[
x > 26
\]

Would you like a detailed explanation or have any questions?

Here are 5 related questions for further practice:

1. Solve the inequality: \( 3x + 7 < 5x - 9 \).
2. Solve the inequality: \( 10x + 15 > 2x - 5 \).
3. Solve the inequality: \( 6x - 3 \leq 9x + 12 \).
4. What is the solution to the inequality \( 5x + 4 \geq 7x - 20 \)?
5. Solve the inequality: \( 2(4x + 1) < 3x - 10 \).

**Tip:** When solving inequalities, keep your work organized by performing one operation at a time on both sides of the inequality.

Learn how to solve the inequality 8x + 4 < 12x - 100 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear inequalities. Suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation