Consider the equation 2over3b+5=−1over3b-4

Solve the equation.

b=b= __

Let's solve the equation step by step:

Given equation:
\[
\frac{2}{3}b + 5 = -\frac{1}{3}b - 4
\]

### Step 1: Eliminate the fractions.
To eliminate the fractions, multiply both sides of the equation by 3 (the common denominator of the fractions):

\[
3 \left( \frac{2}{3}b + 5 \right) = 3 \left( -\frac{1}{3}b - 4 \right)
\]

Simplifying both sides:

\[
2b + 15 = -b - 12
\]

### Step 2: Move all the \(b\)-terms to one side.
Add \(b\) to both sides to collect the \(b\)-terms together:

\[
2b + b + 15 = -b + b - 12
\]

Simplify:

\[
3b + 15 = -12
\]

### Step 3: Isolate \(b\).
Now subtract 15 from both sides:

\[
3b = -12 - 15
\]

Simplify:

\[
3b = -27
\]

### Step 4: Solve for \(b\).
Divide both sides by 3:

\[
b = \frac{-27}{3}
\]

Simplify:

\[
b = -9
\]

Thus, the solution is:
\[
b = -9
\]

Would you like more details, or have any questions?

Here are some related questions:
1. How do you handle equations with variables on both sides?
2. How can you check if a solution to an equation is correct?
3. What is the importance of clearing fractions when solving equations?
4. Can an equation have more than one solution?
5. How do you solve equations involving more complex fractions?

**Tip:** Always verify your solution by plugging it back into the original equation.

Consider the equation 2/3b + 5 = -1/3b - 4. Solve the equation. b = __

Learn how to solve the linear equation 2/3b + 5 = -1/3b - 4 step by step. This solution includes eliminating fractions, combining like terms, and isolating the variable b. Suitable for students in Grades 8-10, covering key algebra concepts.

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