solve for b, -61422.95=(-b/0.99167)(1.230459)+(b/0.99167)

We are tasked with solving for \( b \) in the following equation:

\[
-61422.95 = \left( \frac{-b}{0.99167} \right) \times 1.230459 + \frac{b}{0.99167}
\]

### Step 1: Distribute and simplify
First, distribute both terms on the right-hand side:

\[
-61422.95 = \frac{-b \times 1.230459}{0.99167} + \frac{b}{0.99167}
\]

### Step 2: Combine like terms
Since both terms have the same denominator, we can combine them:

\[
-61422.95 = \frac{-b \times 1.230459 + b}{0.99167}
\]

Factor out \( b \) from the numerator:

\[
-61422.95 = \frac{b(-1.230459 + 1)}{0.99167}
\]

\[
-61422.95 = \frac{b(-0.230459)}{0.99167}
\]

### Step 3: Isolate \( b \)
Multiply both sides by \( 0.99167 \) to eliminate the denominator:

\[
-61422.95 \times 0.99167 = b(-0.230459)
\]

\[
-60889.1605565 = b(-0.230459)
\]

### Step 4: Solve for \( b \)
Now, divide both sides by \( -0.230459 \) to isolate \( b \):

\[
b = \frac{-60889.1605565}{-0.230459}
\]

\[
b \approx 264146.60
\]

### Final Answer:
The value of \( b \) is approximately \( \boxed{264146.60} \).

Would you like further details or clarifications?

Here are 5 related questions for practice:
1. What is the value of \( b \) if the constants change slightly?
2. How do you solve a similar equation if the coefficients are irrational numbers?
3. Can you isolate \( b \) if it appears on both sides without factoring?
4. How would the equation change if instead of addition, it involved subtraction in the second term?
5. What happens to the value of \( b \) if the denominator changes?

**Tip:** Always simplify the equation step-by-step to avoid errors when combining like terms.

Discover how to solve a linear equation involving fractions: -61422.95 = (-b/0.99167)(1.230459) + (b/0.99167). This solution covers key algebraic techniques such as simplification, factoring, and solving for unknown variables. Ideal for students in Grades 9-12.

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