https://r2.erweima.ai/mathbot/image/17259813293158sm4sjxi.jpg

It appears that I wasn't able to extract the mathematical expression directly from the image due to its formatting. However, I can clearly see the equation and will solve it manually.

The equation to solve is:

\[
-\frac{5}{2} = \frac{1}{2}(6x - 1) + \frac{3}{2}x
\]

### Steps to solve for \( x \):

1. **Distribute** the \( \frac{1}{2} \) to both terms inside the parentheses:
   \[
   \frac{1}{2}(6x - 1) = \frac{1}{2}(6x) - \frac{1}{2}(1) = 3x - \frac{1}{2}
   \]
   The equation becomes:
   \[
   -\frac{5}{2} = 3x - \frac{1}{2} + \frac{3}{2}x
   \]

2. **Combine like terms** on the right-hand side:
   \[
   3x + \frac{3}{2}x = \frac{6}{2}x + \frac{3}{2}x = \frac{9}{2}x
   \]
   So the equation is now:
   \[
   -\frac{5}{2} = \frac{9}{2}x - \frac{1}{2}
   \]

3. **Eliminate the fraction** on the right-hand side by adding \( \frac{1}{2} \) to both sides:
   \[
   -\frac{5}{2} + \frac{1}{2} = \frac{9}{2}x
   \]
   Simplify the left-hand side:
   \[
   -\frac{5}{2} + \frac{1}{2} = -\frac{4}{2} = -2
   \]
   Now the equation is:
   \[
   -2 = \frac{9}{2}x
   \]

4. **Solve for \( x \)** by multiplying both sides of the equation by \( \frac{2}{9} \):
   \[
   x = -2 \times \frac{2}{9} = -\frac{4}{9}
   \]

So, the solution is:

\[
x = -\frac{4}{9}
\]

Would you like any further details, or do you have any questions about this solution?

### Related Questions:
1. How do you solve equations with fractions more efficiently?
2. What are some methods for combining like terms in algebraic expressions?
3. Why is it important to distribute multiplication over parentheses in algebra?
4. How can you handle negative numbers in equations without making errors?
5. What are other ways to eliminate fractions when solving equations?

**Tip:** When solving equations with fractions, multiplying the entire equation by the least common denominator (LCD) can simplify the process.

Solve for x: -5/2 = (1/2)(6x - 1) + (3/2)x

Learn how to solve a linear equation with fractions: -5/2 = (1/2)(6x - 1) + (3/2)x. This problem demonstrates the distributive property and combining like terms, suitable 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