Question - Linear Equation in One Variable

To solve the equation \( \frac{3}{4} - \frac{1}{4} x = -5 - \frac{3}{7} - 4x \), first simplify the right side:

Combine \(-5\) and \(-\frac{3}{7}\); convert \(-5\) to have a common denominator:

\(-5 = -\frac{35}{7}\), so \(-5 - \frac{3}{7} = -\frac{35}{7} - \frac{3}{7} = -\frac{38}{7}\)

The equation now reads: \( \frac{3}{4} - \frac{1}{4} x = -\frac{38}{7} - 4x \)

Multiply through by \(28\) (common denominator of \(4\) and \(7\)) to eliminate fractions:

\(28 \cdot \frac{3}{4} - 28 \cdot \frac{1}{4} x = 28 \cdot -\frac{38}{7} - 28 \cdot 4x\)

This simplifies to: \(21 - 7x = -152 - 112x\)

Add \(112x\) to both sides:

\(21 + 105x = -152\)

Now, subtract \(21\) from both sides:

\(105x = -173\)

Finally, divide by \(105\):

\(x = -\frac{173}{105}\)