Solving an Equation with Fractions and Variables
The equation in the image is:
\[ \frac{1}{2} - (8x - 10) + 8 = 2(2x + 2) + 9 \]
First, we should distribute the negative sign through the parentheses on the left side of the equation and distribute the 2 through the parentheses on the right side. This will give us:
\[ \frac{1}{2} - 8x + 10 + 8 = 4x + 4 + 9 \]
Next, combine like terms on each side:
\[ \frac{1}{2} + 10 + 8 = 18 + \frac{1}{2} \]
\[ 18 + \frac{1}{2} - 8x = 4x + 13 \]
Combine the numerical terms on the left side:
\[ 18.5 - 8x = 4x + 13 \]
Next, move all terms containing \( x \) to one side and constant terms to the other side:
\[ 18.5 - 13 = 4x + 8x \]
\[ 5.5 = 12x \]
Finally, divide both sides by 12 to solve for \( x \):
\[ x = \frac{5.5}{12} \]
\[ x = \frac{11}{24} \]
So, \( x = \frac{11}{24} \).
