Ive for \( x \) \( -\frac{5}{4}=\frac{1}{4} x-\frac{2}{3} \) nplify your answer as \( m \)

To solve for \( x \), we start by adding \( \frac{2}{3} \) to both sides of the equation: \[ -\frac{5}{4} + \frac{2}{3} = \frac{1}{4}x \] Now, let's find a common denominator for the fractions on the left side. The least common multiple of 4 and 3 is 12. We convert the fractions: \[ -\frac{5}{4} = -\frac{15}{12}, \quad \text{and} \quad \frac{2}{3} = \frac{8}{12} \] Now we can add them: \[ -\frac{15}{12} + \frac{8}{12} = -\frac{7}{12} \] This gives us: \[ -\frac{7}{12} = \frac{1}{4}x \] Next, we multiply both sides by 4 to isolate \( x \): \[ 4 \cdot -\frac{7}{12} = x \] This simplifies to: \[ -\frac{28}{12} = x \] Now, we can reduce the fraction: \[ x = -\frac{7}{3} \] So, the final answer, expressed as \( m \), is: **\( m = -\frac{7}{3} \)**.