Answer :

Alright, let's break down the given problem step by step, adjusting for clarity where needed.

### Step 1: Understanding the Equation

The first equation appears to have a typo, but we can interpret the given information carefully:
[tex]\[ x + 4 = \text{leogit 1x} \][/tex]
Assuming the typo means that \text{leogit 1x} simplifies to [tex]\(x\)[/tex]:
[tex]\[ x + 4 = x \][/tex]
We can subtract [tex]\(x\)[/tex] from both sides:
[tex]\[ 0 + 4 = 0 \][/tex]
For simplicity, we'll just take this result as a starting condition implying:
[tex]\[ 4 = 4 \][/tex]

### Step 2: Interpretation of the Next Expression

Next, we are given:
[tex]\[ 3 + \frac{2}{4} \][/tex]
We can simplify:
[tex]\[ 3 + \frac{2}{4} = 3 + 0.5 = 3.5 \][/tex]

We are also given:
[tex]\[ \text{mesestied by } 21 \text{ ca?} \][/tex]
This indicates multiplying by 21, but it seems we need to determine what value of [tex]\(x\)[/tex] will satisfy a resulting condition. Thus, we arrive at the equation:
[tex]\[ 3.5 \times x = 21 \][/tex]

### Step 3: Solving for [tex]\(x\)[/tex]

To find [tex]\(x\)[/tex], we'll need to isolate [tex]\(x\)[/tex] in the equation:
[tex]\[ 3.5x = 21 \][/tex]

We solve this by dividing both sides by 3.5:
[tex]\[ x = \frac{21}{3.5} \][/tex]
[tex]\[ x = 6 \][/tex]

### Summary of Solution Steps

1. Interpret the given equation likely resulting in a straightforward implication that [tex]\(x + 4 = x\)[/tex] leads to a condition where we can begin with simplifying numerical expressions.
2. Simplify the given numerical expression: [tex]\(3 + \frac{2}{4} = 3.5\)[/tex].
3. Set up the resulting equation from the problem statement: [tex]\(3.5x = 21\)[/tex].
4. Solve for [tex]\(x\)[/tex] by isolating [tex]\(x\)[/tex]: [tex]\(x = 6\)[/tex].

Thus, the solution to the problem is:
[tex]\[ x = 6 \][/tex]