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Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative StartFraction 7 Over 4 EndFraction – 3x – 5 + 4x = –.

Which step has an incorrect instruction?

Step 1
Step 2
Step 3
Step 4

To determine which step has an incorrect instruction, let's carefully examine each step and compare the instructions with the corresponding mathematical operations. Here’s what the image shows for Deepak's solution:

1. **Step 1: Use the distributive property to simplify.**  
   Resulting equation:  
   \[
   \frac{5}{2} - 5 - 4x - 3x = \frac{-7}{4}
   \]

2. **Step 2: Simplify by combining like terms.**  
   Resulting equation:  
   \[
   \frac{5}{2} - 7x - 5 = \frac{-7}{4}
   \]

3. **Step 3: Use the addition property of equality.**  
   Resulting equation:  
   \[
   \frac{5}{2} - 7x + 5 = \frac{-7}{4} + 5
   \]

4. **Step 4: Use multiplication to find equivalent fractions.**  
   Resulting equation:  
   \[
   \frac{-7x}{2} = \frac{-7}{4} + \frac{10}{2}
   \]

5. **Step 5: Simplify by combining like terms.**  
   Resulting equation:  
   \[
   x = \frac{-3}{4}
   \]

Now let's identify the correct steps:

- **Step 1** correctly applies the distributive property and simplifies.
  
- **Step 2** correctly combines like terms.

- **Step 3** states to use the addition property of equality. However, there is an error here. The addition property should be applied equally to both sides, and it seems like there's a mistake in simplifying the equation after adding 5.

- **Step 4** shows using multiplication to find equivalent fractions, which seems appropriate but should follow correct simplifications.

Given these observations, **Step 3** has the incorrect instruction, as there seems to be a mistake in the simplification after applying the addition property of equality.

Would you like further details or have any questions? Here are five questions to consider:

1. How can we correctly apply the addition property of equality in this context?
2. What would be the correct equation after properly applying the addition property?
3. Could we rework Step 3 with the correct operations?
4. How does each mathematical operation in the steps correspond to basic algebraic principles?
5. Why is it important to verify each step when solving an equation?

**Tip:** Always ensure that each operation is performed consistently on both sides of an equation to maintain equality.

Learn how to identify incorrect instructions in solving equations with a step-by-step analysis of Deepak's solution. This problem covers key algebraic concepts, including equations and properties of equality. Suitable for students in Grades 7-9.

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