Solve the equations by trial-and-error method.
`(3x)/(7)+4=19`

Answer

To solve the equation \(\frac{3x}{7} + 4 = 19\) using the trial-and-error method, we will follow these steps:

### Step 1: Isolate the variable term
First, we need to isolate the term containing \(x\) on one side of the equation. We can do this by subtracting 4 from both sides.

\[ \frac{3x}{7} + 4 - 4 = 19 - 4 \]

This simplifies to:

\[ \frac{3x}{7} = 15 \]

### Step 2: Eliminate the fraction
Next, we will eliminate the fraction by multiplying both sides of the equation by 7.

\[ 7 \cdot \frac{3x}{7} = 15 \cdot 7 \]

This simplifies to:

\[ 3x = 105 \]

### Step 3: Solve for \(x\)
Now, we divide both sides by 3 to solve for \(x\).

\[ x = \frac{105}{3} \]

Calculating this gives:

\[ x = 35 \]

### Step 4: Verify the solution
To ensure our solution is correct, we can substitute \(x = 35\) back into the original equation.

\[ \frac{3(35)}{7} + 4 = 19 \]

Calculating the left-hand side:

\[ \frac{105}{7} + 4 = 15 + 4 = 19 \]

Since both sides are equal, \(x = 35\) is indeed the correct solution.

### Final Answer
The solution to the equation \(\frac{3x}{7} + 4 = 19\) is:

\[ x = 35 \]

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