Let's analyze the inequality from the uploaded image:

The inequality is:

$-2 < -5x + 5 \leq 5$

We need to solve this compound inequality and express the solution in interval notation.

Step 1: Break the compound inequality into two parts

1. Solve $-2 < -5x + 5$
2. Solve $-5x + 5 \leq 5$

Step 2: Solve each part

Part 1: Solve $-2 < -5x + 5$

1. Subtract 5 from both sides: $-2 - 5 < -5x$ $-7 < -5x$
2. Divide by $-5$, remembering to reverse the inequality sign: $\frac{-7}{-5} > x$ $x < \frac{7}{5}$

Part 2: Solve $-5x + 5 \leq 5$

1. Subtract 5 from both sides: $-5x \leq 0$
2. Divide by $-5$, remembering to reverse the inequality sign: $x \geq 0$

Step 3: Combine the solutions

From the two parts, we know: $0 \leq x < \frac{7}{5}$

This means $x$ lies in the interval $[0, \frac{7}{5})$.

Final Answer:

The solution set in interval notation is: $[0, \frac{7}{5})$

Would you like a detailed explanation of any step or further clarification?

Relative Questions:

1. How do you solve compound inequalities involving "less than and equal to"?
2. What are the rules for flipping inequality signs when dividing by a negative number?
3. How do you convert compound inequalities into interval notation?
4. Can we graph the solution of a compound inequality on a number line?
5. What is the difference between closed $[ ]$ and open $( )$ intervals?

Tip:

Always double-check the direction of inequality signs, especially when dividing or multiplying by negative numbers.