2(−𝑎 + 3) −
3
2
(−4𝑎 − 6) = −9

Let's solve the equation step by step:

\[
2(-a + 3) - \frac{3}{2}(-4a - 6) = -9
\]

### Step 1: Distribute the constants
First, distribute the \(2\) and \(\frac{3}{2}\) across the terms inside the parentheses.

\[
2(-a + 3) = 2 \cdot (-a) + 2 \cdot 3 = -2a + 6
\]
\[
\frac{3}{2}(-4a - 6) = \frac{3}{2} \cdot (-4a) + \frac{3}{2} \cdot (-6) = -6a - 9
\]

### Step 2: Substitute back into the equation
Now we substitute these expressions back into the equation:

\[
-2a + 6 - (-6a - 9) = -9
\]

### Step 3: Simplify the equation
Remove the parentheses and simplify:

\[
-2a + 6 + 6a + 9 = -9
\]
Combine like terms:

\[
(6a - 2a) + (6 + 9) = -9
\]
\[
4a + 15 = -9
\]

### Step 4: Solve for \(a\)
Now, subtract 15 from both sides:

\[
4a = -9 - 15
\]
\[
4a = -24
\]
Finally, divide both sides by 4:

\[
a = \frac{-24}{4} = -6
\]

### Final Answer:
\[
a = -6
\]

Would you like further details or have any questions?

Here are some related questions for practice:
1. Solve: \(3(x + 2) - 2(x - 5) = 10\)
2. Solve: \(\frac{2}{3}(3x - 6) - 5 = 7\)
3. Solve: \(5(2 - x) + 3(x + 4) = 12\)
4. Simplify: \(4(a - 2) + 3(2a + 1)\)
5. Solve: \(-\frac{1}{2}(4x - 8) + 5 = -7\)

**Tip:** When distributing negative signs, make sure to distribute to each term within the parentheses to avoid mistakes.

Learn how to solve the linear equation 2(-a + 3) - 3/2(-4a - 6) = -9 using the distributive property and basic algebraic methods. This step-by-step solution explains the process, ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation