Solve `5x - 3 < 7`, when
(i) x is a natural number.
(ii) x is an integer

Explanation

To solve the inequality \(5x - 3 < 7\), we will follow these steps:

### Step 1: Isolate the variable
Start by adding 3 to both sides of the inequality to isolate the term with \(x\).

\[ 5x - 3 + 3 < 7 + 3 \]

This simplifies to:

\[ 5x < 10 \]

### Step 2: Divide by the coefficient of \(x\)
Next, divide both sides of the inequality by 5 to solve for \(x\).

\[ \frac{5x}{5} < \frac{10}{5} \]

This simplifies to:

\[ x < 2 \]

Now we have the solution \(x < 2\).

### Part (i): When \(x\) is a natural number
Natural numbers are the positive integers starting from 1. Therefore, we need to find the natural numbers that satisfy \(x < 2\).

The only natural number less than 2 is:

\[ x = 1 \]

So, the solution for part (i) is:

\[ \text{Natural numbers: } \{1\} \]

### Part (ii): When \(x\) is an integer
Integers include all positive and negative whole numbers, as well as zero. We need to find the integers that satisfy \(x < 2\).

The integers less than 2 are:

\[ \ldots, -3, -2, -1, 0, 1 \]

So, the solution for part (ii) is:

\[ \text{Integers: } \{\ldots, -3, -2, -1, 0, 1\} \]

### Summary of Solutions
- For natural numbers: \( \{1\} \)
- For integers: \( \{\ldots, -3, -2, -1, 0, 1\} \)

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