Questions: Solve. 5z/4 - 2 = z + 3/4 z =

Transcript text: Solve. \[ \begin{array}{l} \frac{5 z}{4}-2=z+\frac{3}{4} \\ z= \end{array} \]

Solution

Solution Steps

To solve the equation \(\frac{5z}{4} - 2 = z + \frac{3}{4}\), we need to isolate the variable \(z\). We can do this by first eliminating the fractions and then solving the resulting linear equation.

Step 1: Combine Like Terms

First, we start with the given equation: \[ \frac{5z}{4} - 2 = z + \frac{3}{4} \]

Step 2: Eliminate Fractions

To eliminate the fractions, we can multiply every term by 4: \[ 4 \left( \frac{5z}{4} \right) - 4 \cdot 2 = 4 \cdot z + 4 \left( \frac{3}{4} \right) \] This simplifies to: \[ 5z - 8 = 4z + 3 \]

Step 3: Isolate the Variable

Next, we isolate \(z\) by subtracting \(4z\) from both sides: \[ 5z - 4z - 8 = 3 \] This simplifies to: \[ z - 8 = 3 \]

Step 4: Solve for \(z\)

Finally, we add 8 to both sides to solve for \(z\): \[ z = 3 + 8 \] \[ z = 11 \]