Solve for X in 4=(2x-1)×2/3: Detailed Linear Equation Solution

To solve this problem, we'll follow these steps:

• Step 1: Eliminate the fraction by multiplying both sides of the equation by the reciprocal of $\frac{2}{3}$.
• Step 2: Simplify the resulting equation.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Multiply both sides of the equation by $\frac{3}{2}$ to eliminate the fraction. This gives:

$\frac{3}{2} \times 4 = \frac{3}{2} \times \left((2x - 1) \times \frac{2}{3}\right)$

Simplifying, the left side becomes:

$6 = 2x - 1$

Step 2: Add 1 to both sides to solve for $2x$:

$6 + 1 = 2x - 1 + 1$

$7 = 2x$

Step 3: Divide both sides by 2 to isolate $x$:

$\frac{7}{2} = x$

Converting $\frac{7}{2}$ to a decimal gives us:

$x = 3.5$

Therefore, the solution to the problem is $x = 3.5$.