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.