If `(5x)/(2)-[7(6x)-3/2]=5/8` then what is the value of x

Options

A. `1/4`
B. `-1/4`
C. 4
D. `-4`

Answer

To solve the equation \(\frac{5x}{2} - [7(6x) - \frac{3}{2}] = \frac{5}{8}\), we will follow these steps:

### Step 1: Simplify the equation
Start with the original equation:
\[ \frac{5x}{2} - [7(6x) - \frac{3}{2}] = \frac{5}{8} \]

### Step 2: Distribute the negative sign
Distributing the negative sign inside the brackets:
\[ \frac{5x}{2} - 7(6x) + \frac{3}{2} = \frac{5}{8} \]

### Step 3: Calculate \(7(6x)\)
Calculate \(7(6x)\):
\[ 7(6x) = 42x \]
So, we rewrite the equation:
\[ \frac{5x}{2} - 42x + \frac{3}{2} = \frac{5}{8} \]

### Step 4: Combine like terms
Combine \(\frac{5x}{2}\) and \(\frac{3}{2}\):
\[ \frac{5x + 3}{2} - 42x = \frac{5}{8} \]

### Step 5: Eliminate the fraction
Multiply the entire equation by 2 to eliminate the fraction:
\[ 5x + 3 - 84x = \frac{5}{4} \]

### Step 6: Combine like terms again
Combine \(5x\) and \(-84x\):
\[ -79x + 3 = \frac{5}{4} \]

### Step 7: Isolate the variable
Subtract 3 from both sides:
\[ -79x = \frac{5}{4} - 3 \]
Convert 3 to a fraction with a denominator of 4:
\[ 3 = \frac{12}{4} \]
So,
\[ -79x = \frac{5}{4} - \frac{12}{4} = \frac{-7}{4} \]

### Step 8: Solve for \(x\)
Divide both sides by -79:
\[ x = \frac{-7}{4} \div -79 = \frac{7}{4 \times 79} = \frac{7}{316} \]

### Final Answer
Thus, the value of \(x\) is:
\[ x = \frac{7}{316} \]