Solve for x:
`(2)/(3)x+1=5`
Represent the solution graphically in each case.

Answer

To solve the equation \(\frac{2}{3}x + 1 = 5\) for \(x\), follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to eliminate the fraction.

\[ 3 \left(\frac{2}{3}x + 1\right) = 3 \cdot 5 \]

### Step 2: Distribute the multiplication
Distributing the 3 on the left side gives us:

\[ 3 \cdot \frac{2}{3}x + 3 \cdot 1 = 15 \]

### Step 3: Simplify the left side
The \(3\) and \(\frac{2}{3}\) cancel out:

\[ 2x + 3 = 15 \]

### Step 4: Isolate the term with \(x\)
Subtract 3 from both sides to isolate the term with \(x\):

\[ 2x = 15 - 3 \]

### Step 5: Simplify the right side
Calculating the right side gives:

\[ 2x = 12 \]

### Step 6: Solve for \(x\)
Now, divide both sides by 2 to find \(x\):

\[ x = \frac{12}{2} \]

### Step 7: Final answer
Thus, we have:

\[ x = 6 \]

### Graphical Representation
To represent the solution graphically on a number line:

1. Draw a horizontal line and mark points at equal intervals.
2. Label the points with integers, including 0, 1, 2, 3, 4, 5, 6, 7, 8, etc.
3. Mark the point corresponding to \(x = 6\) on the number line.