When Ms. Shreve solved 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 analyze Ms. Shreve's work step by step to find the mistake and then solve the equation correctly.

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

### Step 1: Distribute the 5
Ms. Shreve did this correctly.
\[
5(2x - 1) = 10x - 5
\]
So the equation becomes:
\[
10x - 5 - 3x = 5x + 9
\]

### Step 2: Combine like terms on the left side
Again, Ms. Shreve did this correctly.
\[
10x - 3x - 5 = 7x - 5
\]
So the equation becomes:
\[
7x - 5 = 5x + 9
\]

### Step 3: Move all terms involving \(x\) to one side and constant terms to the other side
This is where Ms. Shreve made her mistake.

She should subtract \(5x\) from both sides, but instead, she mistakenly added \(5x\) to \(7x\) (which is not shown), leading to an incorrect next step.

Correctly:
\[
7x - 5x - 5 = 9
\]
This simplifies to:
\[
2x - 5 = 9
\]

### Step 4: Isolate \(x\)
Add 5 to both sides:
\[
2x = 14
\]
Finally, divide by 2:
\[
x = 7
\]

### Conclusion:
Ms. Shreve's mistake was in the step where she incorrectly manipulated the equation to get \(12x = 4\), leading to the wrong solution \(x = 13\). The correct solution is:
\[
\boxed{x = 7}
\]

Would you like more details on any step, or do you have any questions?

### Related Questions:
1. How do you check if a solution is correct in an algebraic equation?
2. What are common mistakes to watch out for when solving linear equations?
3. How can you use the distributive property correctly in algebra?
4. What are like terms, and how do you combine them?
5. Why is it important to isolate the variable when solving an equation?

### Tip:
Always double-check each step, especially when moving terms from one side of an equation to the other, to avoid simple mistakes that can lead to incorrect solutions.

Explore how to identify and correct mistakes in solving linear equations. Analyze a problem where Ms. Shreve incorrectly solved 5(2x - 1) - 3x = 5x + 9, leading to a wrong solution. Learn about algebraic concepts such as the distributive property and combining like terms. Suitable for Grades 7-9.

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