Solve the equations by trial-and-error method.
`(2x)/(5)-3=7`

Answer

To solve the equation \(\frac{2x}{5} - 3 = 7\) using the trial-and-error method, we will follow these steps:

### Step 1: Rearranging the Equation
First, we can rearrange the equation to isolate the term with \(x\):
\[ \frac{2x}{5} = 7 + 3 \]
\[ \frac{2x}{5} = 10 \]

### Step 2: Finding a Suitable Value for \(x\)
Now we will use the trial-and-error method to find a suitable value for \(x\). Since we have a fraction involving 5, we will try multiples of 5 for \(x\).

### Step 3: Trying \(x = 5\)
Let’s start with \(x = 5\):
\[ \frac{2 \times 5}{5} - 3 = 2 - 3 = -1 \quad (\text{not equal to } 7) \]

### Step 4: Trying \(x = 10\)
Next, we try \(x = 10\):
\[ \frac{2 \times 10}{5} - 3 = 4 - 3 = 1 \quad (\text{not equal to } 7) \]

### Step 5: Trying \(x = 15\)
Now, let’s try \(x = 15\):
\[ \frac{2 \times 15}{5} - 3 = 6 - 3 = 3 \quad (\text{not equal to } 7) \]

### Step 6: Trying \(x = 20\)
Next, we try \(x = 20\):
\[ \frac{2 \times 20}{5} - 3 = 8 - 3 = 5 \quad (\text{not equal to } 7) \]

### Step 7: Trying \(x = 25\)
Finally, we try \(x = 25\):
\[ \frac{2 \times 25}{5} - 3 = 10 - 3 = 7 \quad (\text{equal to } 7) \]

### Conclusion
We have found that when \(x = 25\), the equation holds true. Therefore, the solution to the equation \(\frac{2x}{5} - 3 = 7\) is:
\[ \boxed{25} \]