5х-7/12- х-5/8=5
To solve the equation \( 5x - \frac{7}{12} - x - \frac{5}{8} = 5 \), let's simplify it step by step.
Combine like terms: \[ 5x - x = 4x \] So, the equation becomes: \[ 4x - \frac{7}{12} - \frac{5}{8} = 5 \]
To combine the fractions, we need to find a common denominator for \( \frac{7}{12} \) and \( \frac{5}{8} \). The least common multiple of 12 and 8 is 24.
Convert the fractions: \[ \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} \] \[ \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \]
Substitute these values back into the equation: \[ 4x - \frac{14}{24} - \frac{15}{24} = 5 \] \[ 4x - \frac{29}{24} = 5 \]
Next, isolate \( 4x \) by adding \( \frac{29}{24} \) to both sides: \[ 4x = 5 + \frac{29}{24} \]
Convert 5 to a fraction with the denominator of 24: \[ 5 = \frac{120}{24} \] Therefore: \[ 4x = \frac{120}{24} + \frac{29}{24} = \frac{149}{24} \]
Finally, divide both sides by 4: \[ x = \frac{149}{24} \cdot \frac{1}{4} = \frac{149}{96} \]
Thus, the solution to the equation is: \[ x = \frac{149}{96} \]
