ved an equation in class, she checked her solution and it did not make the equation true! Examine her work below and find her mistake. Then find the correct solution. Homework Help ✎
 5(2𝑥 − 1) − 3𝑥 = 5𝑥 + 9 10𝑥 − 5 − 3𝑥 = 5𝑥 + 9 7𝑥 − 5 = 5𝑥 + 9
12𝑥 = 4
𝑥 = 13

Let's go through Ved's solution step-by-step to find the mistake and then solve the equation correctly.

### Original Equation:
\[
5(2x - 1) - 3x = 5x + 9
\]

### Step-by-Step Analysis

1. **Distribute and Simplify:**
   \[
   5(2x - 1) - 3x = 5x + 9
   \]
   Distribute the 5:
   \[
   10x - 5 - 3x = 5x + 9
   \]

2. **Combine Like Terms:**
   \[
   (10x - 3x) - 5 = 5x + 9
   \]
   Simplify:
   \[
   7x - 5 = 5x + 9
   \]

3. **Isolate \(x\):**
   Subtract \(5x\) from both sides:
   \[
   7x - 5x - 5 = 9
   \]
   This simplifies to:
   \[
   2x - 5 = 9
   \]

4. **Add 5 to Both Sides:**
   \[
   2x - 5 + 5 = 9 + 5
   \]
   Simplify:
   \[
   2x = 14
   \]

5. **Divide by 2:**
   \[
   x = \frac{14}{2}
   \]
   Simplify:
   \[
   x = 7
   \]

### Identifying Ved's Mistake:
Ved made an error after the step where she had:
\[
7x - 5 = 5x + 9
\]
She incorrectly simplified or made an algebraic mistake leading to:
\[
12x = 4 \quad \text{and} \quad x = 13
\]
These steps are incorrect because they do not follow from any logical algebraic manipulation of the terms.

### Correct Solution:
The correct value of \(x\) is:

\[
x = 7
\]

Ved should have followed the correct algebraic steps as shown above.

Would you like further details or have any questions about the solution? 

Here are some related questions to consider:

1. How do you distribute terms in algebraic expressions?
2. What is the importance of combining like terms in an equation?
3. How can you check your solution to ensure it satisfies the original equation?
4. What steps are involved in isolating a variable in an equation?
5. How can errors in solving equations impact the interpretation of results?

**Tip:** Always double-check each step when solving an equation to ensure that all algebraic operations are performed correctly.

Discover how to identify and correct mistakes in solving algebraic equations. Explore a detailed analysis of an equation problem and learn essential algebraic techniques such as distributing terms, combining like terms, and isolating variables. Suitable for Grades 7-9 students.

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