`-1/8 (8-10x) gt 3x -2`
Which of the following describes all possible values of x ?

Options

A. `x lt -12/7`
B. `x gt -4/7`
C. `x lt 4/7`
D. `x gt 4/7`

Explanation

To solve the inequality \(-\frac{1}{8}(8 - 10x) > 3x - 2\), we will follow these steps:

### Step 1: Distribute the left side of the inequality
We start by distributing \(-\frac{1}{8}\) across the expression inside the parentheses:

\[ -\frac{1}{8} \cdot 8 + \frac{1}{8} \cdot 10x > 3x - 2 \]

This simplifies to:

\[ -1 + \frac{10}{8}x > 3x - 2 \]

### Step 2: Simplify the fraction
Next, we simplify \(\frac{10}{8}x\):

\[ -1 + \frac{5}{4}x > 3x - 2 \]

### Step 3: Move all terms involving \(x\) to one side
Now we will move all \(x\) terms to one side and constant terms to the other side. We can do this by subtracting \(3x\) from both sides:

\[ -1 + \frac{5}{4}x - 3x > -2 \]

### Step 4: Combine like terms
To combine the \(x\) terms, we convert \(3x\) into a fraction with a denominator of 4:

\[ -1 + \frac{5}{4}x - \frac{12}{4}x > -2 \]

This gives us:

\[ -1 - \frac{7}{4}x > -2 \]

### Step 5: Move the constant term to the right side
Next, we add 1 to both sides:

\[ -\frac{7}{4}x > -2 + 1 \]

This simplifies to:

\[ -\frac{7}{4}x > -1 \]

### Step 6: Multiply by -1 and reverse the inequality
Since we are multiplying by a negative number, we must reverse the inequality:

\[ \frac{7}{4}x < 1 \]

### Step 7: Isolate \(x\)
Now, we multiply both sides by \(\frac{4}{7}\):

\[ x < \frac{4}{7} \]

### Conclusion
The solution to the inequality is:

\[ x < \frac{4}{7} \]

This means that all possible values of \(x\) are less than \(\frac{4}{7}\).

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