Let's solve the equation step by step:

### Given:
\[
2\left(\frac{1}{2}q + 1\right) = -3(2q - 1) + 8q + 4
\]

### Step 1: Distribute the constants on both sides.
First, distribute \(2\) on the left side and \(-3\) on the right side.

\[
2 \times \frac{1}{2}q + 2 \times 1 = -3 \times 2q + (-3) \times (-1) + 8q + 4
\]

This simplifies to:
\[
q + 2 = -6q + 3 + 8q + 4
\]

### Step 2: Combine like terms.
On the right side, combine the \(q\) terms and the constants:

\[
q + 2 = (-6q + 8q) + (3 + 4)
\]

\[
q + 2 = 2q + 7
\]

### Step 3: Solve for \(q\).
Now, subtract \(q\) from both sides:

\[
2 = q + 7
\]

Next, subtract 7 from both sides:

\[
2 - 7 = q
\]

\[
q = -5
\]

### Final Answer:
\[
q = -5
\]

Do you need further details or have any questions?

Here are five follow-up questions to deepen your understanding:
1. How do you distribute a constant over parentheses?
2. What happens when you combine like terms involving variables?
3. How do you isolate a variable when it's on both sides of an equation?
4. What does it mean to simplify an expression?
5. Can you solve an equation with fractions directly without clearing them?

**Tip**: Always double-check your work by substituting the solution back into the original equation to verify it satisfies both sides.

Learn how to solve the linear equation 2(1/2q + 1) = -3(2q - 1) + 8q + 4 using the distributive property and combining like terms. Follow a detailed step-by-step solution to find q = -5, designed 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