Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Question

What value of p makes the equation true?
-3x-6+1/8=-1/4


p =

Answer 1

To solve the equation \(-3x - 6 + \frac{1}{8} = -\frac{1}{4}\), we first isolate \(x\).

1. Start by combining constants on the left side: \[ -3x - 6 + \frac{1}{8} = -\frac{1}{4} \]

2. To combine \(-6\) and \(\frac{1}{8}\), we convert \(-6\) to a fraction: \[ -6 = -\frac{48}{8} \] So, \[ -3x - \frac{48}{8} + \frac{1}{8} = -\frac{1}{4} \]

3. Combine the fractions on the left side: \[ -3x - \frac{48}{8} + \frac{1}{8} = -3x - \frac{47}{8} \]

4. Now we have: \[ -3x - \frac{47}{8} = -\frac{1}{4} \]

5. Convert \(-\frac{1}{4}\) to a fraction with a denominator of 8: \[ -\frac{1}{4} = -\frac{2}{8} \]

6. Substitute this back into the equation: \[ -3x - \frac{47}{8} = -\frac{2}{8} \]

7. Add \(\frac{47}{8}\) to both sides: \[ -3x = -\frac{2}{8} + \frac{47}{8} \] \[ -3x = \frac{45}{8} \]

8. Divide both sides by -3: \[ x = \frac{45}{8} \times -\frac{1}{3} = -\frac{45}{24} \]

9. Simplify \(-\frac{45}{24}\): \[ x = -\frac{15}{8} \]

Thus, the value of \(p\) that makes the equation true is: \[ p = -\frac{15}{8} \]