Questions: Solve: -4/7 b + 1/4 = 1/3 b + 1/2.

Solve: -4/7 b + 1/4 = 1/3 b + 1/2.
Transcript text: Solve: $-\frac{4}{7} b+\frac{1}{4}=\frac{1}{3} b+\frac{1}{2}$.
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Solution

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Solution Steps

To solve the equation \(-\frac{4}{7} b + \frac{1}{4} = \frac{1}{3} b + \frac{1}{2}\), we need to isolate the variable \(b\). This involves moving all terms containing \(b\) to one side of the equation and the constant terms to the other side. Then, we can solve for \(b\) by combining like terms and simplifying.

Step 1: Combine Like Terms

First, we start with the given equation: \[ -\frac{4}{7} b + \frac{1}{4} = \frac{1}{3} b + \frac{1}{2} \]

Step 2: Move All Terms Involving \( b \) to One Side

We move all terms involving \( b \) to one side and constants to the other side: \[ -\frac{4}{7} b - \frac{1}{3} b = \frac{1}{2} - \frac{1}{4} \]

Step 3: Simplify Both Sides

Combine the terms involving \( b \) and the constants: \[ -\left(\frac{4}{7} + \frac{1}{3}\right) b = \frac{1}{2} - \frac{1}{4} \]

Step 4: Find a Common Denominator and Simplify

Find a common denominator for the fractions: \[ -\left(\frac{12}{21} + \frac{7}{21}\right) b = \frac{2}{4} - \frac{1}{4} \] \[ -\left(\frac{19}{21}\right) b = \frac{1}{4} \]

Step 5: Solve for \( b \)

Isolate \( b \) by dividing both sides by \(-\frac{19}{21}\): \[ b = \frac{\frac{1}{4}}{-\frac{19}{21}} \] \[ b = \frac{1}{4} \times -\frac{21}{19} \] \[ b = -\frac{21}{76} \]

Final Answer

\[ \boxed{b = -\frac{21}{76}} \]

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