Let's solve the equation step by step. The original equation is:
\[ \frac{3}{4}x + 3 - 2x = -\frac{1}{4} + \frac{1}{2}x + 5 \]
You correctly combined terms and arrived at:
\[ -\frac{5}{4}x + 3 = \frac{19}{4} + \frac{1}{2}x \]
Now, let's continue from there.
Step 1: Get all the \(x\) terms on one side and the constant terms on the other side. To do this, add \(\frac{5}{4}x\) to both sides and subtract \(\frac{19}{4}\) from both sides.
\[ 3 - \frac{19}{4} = \frac{1}{2}x + \frac{5}{4}x \]
Step 2: Convert 3 to a fraction with a denominator of 4:
\[ \frac{12}{4} - \frac{19}{4} = \frac{1}{2}x + \frac{5}{4}x \]
Step 3: Simplify the left side:
\[ \frac{12 - 19}{4} = \frac{1}{2}x + \frac{5}{4}x \] \[ \frac{-7}{4} = \frac{1}{2}x + \frac{5}{4}x \]
Step 4: Convert \(\frac{1}{2}x\) to have a common denominator of 4:
\[ \frac{1}{2}x = \frac{2}{4}x \]
Now rewrite the equation:
\[ \frac{-7}{4} = \frac{2}{4}x + \frac{5}{4}x \]
Step 5: Combine the \(x\) terms on the right:
\[ \frac{-7}{4} = \frac{7}{4}x \]
Step 6: To isolate \(x\), multiply both sides by \(\frac{4}{7}\):
\[ x = \frac{-7}{4} \cdot \frac{4}{7} \]
Step 7: Simplify:
\[ x = -1 \]
So the solution to the equation is:
\[ x = -1 \]