If `2x+5/3=1/4x+4`, then x=?

Answer

To solve the equation \(2x + \frac{5}{3} = \frac{1}{4}x + 4\), we will follow these steps:

### Step 1: Rearranging the equation
We start by moving all terms involving \(x\) to one side and the constant terms to the other side.

\[ 2x - \frac{1}{4}x = 4 - \frac{5}{3} \]

### Step 2: Finding a common denominator
To simplify the left side, we need to find a common denominator for the fractions. The common denominator for \(1\) and \(4\) is \(4\).

\[ 2x = \frac{8}{4}x \]

Now, substituting this into our equation gives us:

\[ \frac{8}{4}x - \frac{1}{4}x = 4 - \frac{5}{3} \]

### Step 3: Simplifying the left side
Now we can combine the \(x\) terms on the left side:

\[ \frac{8x - 1x}{4} = \frac{7x}{4} \]

### Step 4: Simplifying the right side
Next, we simplify the right side. To do this, we need to find a common denominator for \(4\) and \(3\), which is \(12\):

\[ 4 = \frac{48}{12} \quad \text{and} \quad \frac{5}{3} = \frac{20}{12} \]

So, we can rewrite the right side:

\[ 4 - \frac{5}{3} = \frac{48}{12} - \frac{20}{12} = \frac{28}{12} \]

### Step 5: Equating both sides
Now we have:

\[ \frac{7x}{4} = \frac{28}{12} \]

### Step 6: Cross-multiplying
To eliminate the fractions, we cross-multiply:

\[ 7x \cdot 12 = 28 \cdot 4 \]

This simplifies to:

\[ 84x = 112 \]

### Step 7: Solving for \(x\)
Now, divide both sides by \(84\):

\[ x = \frac{112}{84} \]

### Step 8: Simplifying the fraction
We can simplify \(\frac{112}{84}\) by dividing both the numerator and the denominator by \(28\):

\[ x = \frac{4}{3} \]

### Final Answer
Thus, the solution to the equation is:

\[ \boxed{\frac{4}{3}} \]