Question

1)
\frac{8x - 4}{2} = 2x + 6

Explanation:

Step1: Simplify the left - hand side

We can split the fraction $\frac{8x - 4}{2}$ into two separate fractions: $\frac{8x}{2}-\frac{4}{2}$.
Simplifying each fraction, we get $4x - 2$. So the equation becomes $4x-2 = 2x + 6$.

Step2: Subtract $2x$ from both sides

To get all the $x$ terms on one side, we subtract $2x$ from both sides of the equation $4x-2 = 2x + 6$.
$(4x-2)-2x=(2x + 6)-2x$.
Simplifying both sides: $4x-2x-2=2x-2x + 6$, which gives $2x-2=6$.

Step3: Add 2 to both sides

To isolate the term with $x$, we add 2 to both sides of the equation $2x-2=6$.
$(2x - 2)+2=6 + 2$.
Simplifying both sides: $2x=8$.

Step4: Divide both sides by 2

To solve for $x$, we divide both sides of the equation $2x = 8$ by 2.
$\frac{2x}{2}=\frac{8}{2}$.
Simplifying both sides gives $x = 4$.

Answer:

$x = 4$