What value of x satisties the equation `(2)/(3)(5x+7)=8x?`

Answer

To solve the equation \(\frac{2}{3}(5x + 7) = 8x\), we will follow these steps:

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

\[ 3 \cdot \frac{2}{3}(5x + 7) = 3 \cdot 8x \]

This simplifies to:

\[ 2(5x + 7) = 24x \]

### Step 2: Distribute on the left side
Now, distribute the 2 on the left side.

\[ 2 \cdot 5x + 2 \cdot 7 = 24x \]

This simplifies to:

\[ 10x + 14 = 24x \]

### Step 3: Move all terms involving \(x\) to one side
Subtract \(10x\) from both sides to get all \(x\) terms on one side.

\[ 14 = 24x - 10x \]

This simplifies to:

\[ 14 = 14x \]

### Step 4: Solve for \(x\)
Now, divide both sides by 14 to isolate \(x\).

\[ x = \frac{14}{14} \]

This simplifies to:

\[ x = 1 \]

### Final Answer
The value of \(x\) that satisfies the equation is:

\[ \boxed{1} \]

---