Question - Solving an Equation with Fractions and Variables
Solution:
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, $$ x = \frac{11}{24} $$.
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