Solve the Linear Equation: 5(X-8) + 1/2 = 0

To solve the linear equation $5(x-8)+\frac{1}{2}=0$, follow these steps:

• Step 1: Distribute the 5 across $(x-8)$.

The equation becomes:

$5x - 40 + \frac{1}{2} = 0$.

• Step 2: Combine the constants on the left side.

Combine $-40$ and $\frac{1}{2}$:

$5x - 40 + \frac{1}{2} = 0$.

Convert $-40$ into a fraction to simplify: $-40 = -\frac{80}{2}$.

The equation becomes:

$5x - \frac{80}{2} + \frac{1}{2} = 0$.

Simplify it to:

$5x - \frac{79}{2} = 0$.

• Step 3: Isolate $x$.

To move $-\frac{79}{2}$ to the other side, we add $\frac{79}{2}$ to both sides:

$5x = \frac{79}{2}$.

• Step 4: Solve for $x$.

Divide both sides by 5 to isolate $x$:

$x = \frac{79}{2} \div 5$.

$x = \frac{79}{2} \times \frac{1}{5}$.

$x = \frac{79}{10}$.

Therefore, the solution to the equation is $x = \frac{79}{10}$.