Solve :
`x+7-(8x)/(3)=(17x)/(6)-(5x)/(8)`

Answer

To solve the equation \( x + 7 - \frac{8x}{3} = \frac{17x}{6} - \frac{5x}{8} \), we will follow these steps:

### Step 1: Move all terms involving \( x \) to the left side and constant terms to the right side.

Starting with the equation:
\[ x + 7 - \frac{8x}{3} = \frac{17x}{6} - \frac{5x}{8} \]

We can rearrange it as:
\[ x - \frac{8x}{3} - \frac{17x}{6} + \frac{5x}{8} = -7 \]

### Step 2: Find a common denominator for the fractions.

The denominators are 3, 6, and 8. The least common multiple (LCM) of these numbers is 24. We will express each term with a denominator of 24:

- \( x = \frac{24x}{24} \)
- \( -\frac{8x}{3} = -\frac{64x}{24} \) (since \( 8 \times 8 = 64 \))
- \( -\frac{17x}{6} = -\frac{68x}{24} \) (since \( 17 \times 4 = 68 \))
- \( \frac{5x}{8} = \frac{15x}{24} \) (since \( 5 \times 3 = 15 \))

Now substituting these back into the equation gives:
\[ \frac{24x}{24} - \frac{64x}{24} - \frac{68x}{24} + \frac{15x}{24} = -7 \]

### Step 3: Combine the terms on the left side.

Combining the \( x \) terms:
\[ \frac{24x - 64x - 68x + 15x}{24} = -7 \]

Calculating the numerator:
\[ 24 - 64 - 68 + 15 = -93 \]

So we have:
\[ \frac{-93x}{24} = -7 \]

### Step 4: Eliminate the fraction by multiplying both sides by 24.

\[ -93x = -7 \times 24 \]

Calculating the right side:
\[ -7 \times 24 = -168 \]

So we get:
\[ -93x = -168 \]

### Step 5: Solve for \( x \).

Dividing both sides by -93:
\[ x = \frac{-168}{-93} = \frac{168}{93} \]

### Step 6: Simplify the fraction.

To simplify \( \frac{168}{93} \), we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:
\[ x = \frac{168 \div 3}{93 \div 3} = \frac{56}{31} \]

### Final Answer:
\[ x = \frac{56}{31} \]

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