The following are the steps involved in solving the equation`(8x+7)/(15)+(3x+7)/(10)=2`. Arrange them in sequential order.
(A) The LCM of 15 and 10 is 30.
(B) `25x+35=60`
(C ) Given `(8x+7)/(15)+(3x+7)/(10)=2`
(D) `(2(8x+7)+3(3x+7))/(30)=2`
(E) `x=1`

Options

A. CEADB
B. CBADE
C. CADBE
D. CDAEB

Answer

To solve the equation \(\frac{8x + 7}{15} + \frac{3x + 7}{10} = 2\) and arrange the steps in sequential order, we can follow these steps:

### Step-by-Step Solution:

1. **Write the given equation**:
\[ \frac{8x + 7}{15} + \frac{3x + 7}{10} = 2 \]
This corresponds to step (C).

2. **Find the LCM of the denominators**:
The denominators are 15 and 10. The least common multiple (LCM) of 15 and 10 is 30.
This corresponds to step (A).

3. **Rewrite the equation using the LCM**:
We can express the equation with a common denominator:
\[ \frac{2(8x + 7)}{30} + \frac{3(3x + 7)}{30} = 2 \]
This corresponds to step (D).

4. **Combine the fractions**:
Now, combine the fractions:
\[ \frac{2(8x + 7) + 3(3x + 7)}{30} = 2 \]
Simplifying the left side:
\[ 2(8x + 7) = 16x + 14 \quad \text{and} \quad 3(3x + 7) = 9x + 21 \]
So, we have:
\[ \frac{16x + 14 + 9x + 21}{30} = 2 \]
Combine like terms:
\[ \frac{25x + 35}{30} = 2 \]
This corresponds to step (B).

5. **Clear the fraction by multiplying both sides by 30**:
\[ 25x + 35 = 60 \]

6. **Solve for \(x\)**:
Subtract 35 from both sides:
\[ 25x = 60 - 35 \]
\[ 25x = 25 \]
Divide by 25:
\[ x = 1 \]
This corresponds to step (E).

### Final Order of Steps:
The correct order of steps is:
- (C) Given \(\frac{8x + 7}{15} + \frac{3x + 7}{10} = 2\)
- (A) The LCM of 15 and 10 is 30.
- (D) \(\frac{2(8x + 7) + 3(3x + 7)}{30} = 2\)
- (B) \(25x + 35 = 60\)
- (E) \(x = 1\)