If `root(3)(5j-7)=-(1)/(2)`, what is the value of j ?

Options

A. `1.375`
B. `2.118`
C. `2.599`
D. `5.125`

Explanation

To solve the equation \( \sqrt[3]{5j - 7} = -\frac{1}{2} \), we will follow these steps:

### Step 1: Remove the cube root
To eliminate the cube root, we will raise both sides of the equation to the power of 3.

\[ \left(\sqrt[3]{5j - 7}\right)^3 = \left(-\frac{1}{2}\right)^3 \]

### Step 2: Simplify both sides
The left side simplifies to \( 5j - 7 \), and the right side simplifies to \( -\frac{1}{8} \).

\[ 5j - 7 = -\frac{1}{8} \]

### Step 3: Isolate the term with \( j \)
Next, we will add 7 to both sides to isolate the term with \( j \).

\[ 5j = -\frac{1}{8} + 7 \]

### Step 4: Convert 7 to a fraction
To perform the addition, we need to express 7 as a fraction with a denominator of 8.

\[ 7 = \frac{56}{8} \]

Now substituting this back into the equation:

\[ 5j = -\frac{1}{8} + \frac{56}{8} \]

### Step 5: Combine the fractions
Now we can combine the fractions on the right side.

\[ 5j = \frac{56 - 1}{8} = \frac{55}{8} \]

### Step 6: Solve for \( j \)
Now, we will divide both sides by 5 to solve for \( j \).

\[ j = \frac{55}{8} \div 5 = \frac{55}{8} \cdot \frac{1}{5} = \frac{55}{40} \]

### Step 7: Simplify the fraction
Now we can simplify \( \frac{55}{40} \).

\[ j = \frac{11}{8} \]

### Final Result
Thus, the value of \( j \) is \( \frac{11}{8} \) or \( 1.375 \).

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