5х-7/12- х-5/8=5
To solve the equation
\[ 5x - \frac{7}{12} - x - \frac{5}{8} = 5, \]
we can first simplify the equation by combining like terms.
- Combine the \( x \) terms:
\[ (5x - x) - \frac{7}{12} - \frac{5}{8} = 5. \]
This simplifies to:
\[ 4x - \frac{7}{12} - \frac{5}{8} = 5. \]
- Now, let's find a common denominator for the fractions \(\frac{7}{12}\) and \(\frac{5}{8}\). The least common multiple of 12 and 8 is 24.
Now, we convert each fraction:
\[ \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} \]
\[ \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}. \]
Now substitute these values back into the equation:
\[ 4x - \frac{14}{24} - \frac{15}{24} = 5. \]
Combine the fractions:
\[ 4x - \frac{14 + 15}{24} = 5, \] \[ 4x - \frac{29}{24} = 5. \]
- Now, add \(\frac{29}{24}\) to both sides of the equation:
\[ 4x = 5 + \frac{29}{24}. \]
Convert 5 to a fraction with a denominator of 24:
\[ 5 = \frac{120}{24}, \]
So,
\[ 4x = \frac{120}{24} + \frac{29}{24} = \frac{149}{24}. \]
- Finally, divide both sides by 4:
\[ x = \frac{149}{24} \div 4 = \frac{149}{96}. \]
Thus, the solution is:
\[ x = \frac{149}{96}. \]
