if `2z+8/3=1/4z+5`, then z=?

Options

A. `3`
B. `4`
C. `3/4`
D. `4/3`

Answer

To solve the equation \(2z + \frac{8}{3} = \frac{1}{4}z + 5\), we will follow these steps:

### Step 1: Move all terms involving \(z\) to one side and constant terms to the other side.
We can rearrange the equation:
\[ 2z - \frac{1}{4}z = 5 - \frac{8}{3} \]

### Step 2: Simplify the left side.
To combine \(2z\) and \(-\frac{1}{4}z\), we need a common denominator. The common denominator for 1 and 4 is 4:
\[ 2z = \frac{8}{4}z \]
Now, substituting this back into the equation gives:
\[ \frac{8}{4}z - \frac{1}{4}z = 5 - \frac{8}{3} \]
This simplifies to:
\[ \frac{7}{4}z = 5 - \frac{8}{3} \]

### Step 3: Simplify the right side.
To subtract \(5\) and \(\frac{8}{3}\), we convert \(5\) into a fraction with a denominator of 3:
\[ 5 = \frac{15}{3} \]
Now, substituting gives:
\[ \frac{7}{4}z = \frac{15}{3} - \frac{8}{3} = \frac{15 - 8}{3} = \frac{7}{3} \]

### Step 4: Solve for \(z\).
Now we have:
\[ \frac{7}{4}z = \frac{7}{3} \]
To isolate \(z\), multiply both sides by the reciprocal of \(\frac{7}{4}\):
\[ z = \frac{7}{3} \times \frac{4}{7} \]
The \(7\) cancels out:
\[ z = \frac{4}{3} \]

### Final Answer:
Thus, the value of \(z\) is:
\[ \boxed{\frac{4}{3}} \]