Questions: 3/4 j-2(1/2 j+2)=1/8 j j=

Solution Steps

To solve the equation \(\frac{3}{4} j - 2\left(\frac{1}{2} j + 2\right) = \frac{1}{8} j\), we need to follow these steps:

1. Distribute the \(-2\) through the parentheses.
2. Combine like terms on the left side of the equation.
3. Move all terms involving \(j\) to one side of the equation.
4. Solve for \(j\) by isolating it.

Starting with the equation: \[ \frac{3}{4} j - 2\left(\frac{1}{2} j + 2\right) = \frac{1}{8} j \] we distribute \(-2\) through the parentheses: \[ \frac{3}{4} j - (j + 4) = \frac{1}{8} j \]

Now, we simplify the left side: \[ \frac{3}{4} j - j - 4 = \frac{1}{8} j \] This can be rewritten as: \[ \left(\frac{3}{4} - 1\right) j - 4 = \frac{1}{8} j \] which simplifies to: \[ -\frac{1}{4} j - 4 = \frac{1}{8} j \]

Next, we move all terms involving \(j\) to one side: \[ -\frac{1}{4} j - \frac{1}{8} j = 4 \] To combine the \(j\) terms, we find a common denominator: \[ -\frac{2}{8} j - \frac{1}{8} j = 4 \] This simplifies to: \[ -\frac{3}{8} j = 4 \]

Now, we isolate \(j\) by multiplying both sides by \(-\frac{8}{3}\): \[ j = -\frac{8}{3} \cdot 4 = -\frac{32}{3} \] This can also be expressed as: \[ j \approx -10.6667 \]

Final Answer