https://file.aiquickdraw.com/mathbot/file/1726598369306vbtpt6o4.jpg

The image you uploaded contains a complex inequality expression involving fractions and variables. I will transcribe and solve the inequality step by step.

The inequality is as follows:

\[
\frac{5x - (3x - 2) - 2.5 \left( 2 - \frac{x}{3} \right) + 5x}{20} \leq \frac{2x - \frac{1}{5} - 3(5x - 2) - 3x}{15}
\]

### Step-by-Step Solution

1. **Simplify each side separately:**

- On the left side:
  \[
  5x - (3x - 2) = 5x - 3x + 2 = 2x + 2
  \]
  Also, simplify the term with the fraction:
  \[
  -2.5 \left( 2 - \frac{x}{3} \right) = -2.5(2) + 2.5\left( \frac{x}{3} \right) = -5 + \frac{2.5x}{3}
  \]
  Putting this all together, the left side becomes:
  \[
  \frac{2x + 2 - 5 + \frac{2.5x}{3} + 5x}{20} = \frac{7x - 3 + \frac{2.5x}{3}}{20}
  \]

- On the right side:
  Simplify each term:
  \[
  3(5x - 2) = 15x - 6
  \]
  The right side becomes:
  \[
  \frac{2x - \frac{1}{5} - 15x + 6 - 3x}{15} = \frac{-16x + 6 - \frac{1}{5}}{15}
  \]

2. **Clear the denominators by multiplying both sides by the least common denominator (LCM of 20 and 15, which is 60):**

Multiplying each side by 60 to eliminate the fractions.

Let me proceed with this simplification.After multiplying both sides by 60, we get the following simplified inequality:

\[
23.5x - 9 \leq 23.2 - 64x
\]

### Step-by-Step Solution from Here:

3. **Move all terms involving \(x\) to one side and constants to the other side:**
\[
23.5x + 64x \leq 23.2 + 9
\]
\[
87.5x \leq 32.2
\]

4. **Solve for \(x\):**
\[
x \leq \frac{32.2}{87.5}
\]
\[
x \leq 0.368
\]

Thus, the solution to the inequality is:
\[
x \leq 0.368
\]

Would you like more details or clarification on any steps?

Here are 5 related questions:
1. How do you handle inequalities with fractions?
2. What is the significance of multiplying by the least common denominator (LCD)?
3. Can this inequality solution be plotted on a number line?
4. How do we handle inequalities when multiplying or dividing by negative numbers?
5. What happens when the inequality involves absolute values?

**Tip**: Always check for sign changes when multiplying or dividing both sides of an inequality by negative values.

Solve the inequality: (5x - (3x - 2) - 2.5(2 - x/3) + 5x)/20 ≤ (2x - 1/5 - 3(5x - 2) - 3x)/15

Learn how to solve an algebraic inequality involving variables and fractions step by step. This example demonstrates clearing fractions, simplifying terms, and solving for the variable x, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation