Answer
$x = 0.9375$
Method 1
Work Step by Step
$2(4-8x)+6=-1$
Method $1$: One way to solve the equation is by using the Distributive Property.
$$\begin{align*}
2(4-8x)+6&=-1\\
2(4) - 2(8x)+6&=-1&&\text{Distributive Property}\\
8 - 16x +6 &=-1&&\text{Multiply}\\
14- 16x &=-1&&\text{Combine like items}\\
-16x &= -1-14&&\text{Subtract }14\text{ from each side}\\
16x& =15\\
x&=\frac{15}{16}&&\text{Divide each side by } 16\\
x&=0.9375&&\text{Simplify}
\end{align*}$$
Method $2$: Another way to solve the equation is by interpreting the expression $(4-8x)$ as a single quantity.
$$\begin{align*}
2(4-8x)+6&=-1\\
2(4-8x)+6-6&=-1-6&&\text{Subtract }6 \text{ from each side}\\
2(4-8x)&=-7&&\text{Simplif}\\
\frac{2(4-8x)}{2}& = \frac{-7}{2}&&\text{Divide each side by } 2\\
4-8x &= -3.5&&\text{Simplify}\\
4-8x-4 &= -3.5-4&&\text{Subtract }4\text{ from each side}\\
-8x &= -7.5&&\text{Divide each side by }-1\\
8x &= 7.5&&\text{Divide each side by }8\\
x &= \frac{7.5}{8}&&\text{Simplify}\\
x& = 0.9375
\end{align*}$$
We will prefer the method $1$ as it is very easy and convenient as compared to method $2$.
