Find the solution of the following equations by trial-and-error method.
`3x-5=34`

Answer

To solve the equation \(3x - 5 = 34\) using the trial-and-error method, we will follow these steps:

### Step 1: Understand the equation
We have the equation \(3x - 5 = 34\). Our goal is to find the value of \(x\) that makes the left-hand side (LHS) equal to the right-hand side (RHS).

### Step 2: Start with a guess for \(x\)
Let's start by guessing a value for \(x\). We can begin with \(x = 5\).

### Step 3: Calculate LHS for \(x = 5\)
Substituting \(x = 5\) into the equation:
\[ LHS = 3(5) - 5 = 15 - 5 = 10 \]
Since \(10\) is not equal to \(34\), we conclude that \(x\) is not \(5\).

### Step 4: Try a larger value for \(x\)
Next, let's try \(x = 11\):
\[ LHS = 3(11) - 5 = 33 - 5 = 28 \]
Since \(28\) is not equal to \(34\), we conclude that \(x\) is not \(11\).

### Step 5: Continue trying larger values
Now, let's try \(x = 12\):
\[ LHS = 3(12) - 5 = 36 - 5 = 31 \]
Since \(31\) is not equal to \(34\), we conclude that \(x\) is not \(12\).

### Step 6: Try \(x = 13\)
Now, let's try \(x = 13\):
\[ LHS = 3(13) - 5 = 39 - 5 = 34 \]
Since \(34\) is equal to \(34\), we have found our solution.

### Conclusion
Thus, the solution to the equation \(3x - 5 = 34\) is:
\[ x = 13 \]