To simplify the original equation and determine which option is equivalent, follow these steps:
1. Combine Like Terms:
The original equation given is:
[tex]\[
15x - 5 + x = -47
\][/tex]
Combine the terms involving \( x \).
[tex]\[
15x + x - 5 = -47
\][/tex]
Simplify the expression on the left-hand side:
[tex]\[
(15 + 1)x - 5 = -47
\][/tex]
[tex]\[
16x - 5 = -47
\][/tex]
2. Write the Simplified Equation:
The simplified equation is:
[tex]\[
16x - 5 = -47
\][/tex]
3. Compare with Given Choices:
Now, compare the simplified equation with the options provided:
- A: \( 16x - 5 = -47 \)
- B: \( 11x = -47 \)
- C: \( 14x - 5 = -47 \)
- D: \( 21x = -47 \)
The simplified equation \( 16x - 5 = -47 \) matches option A.
Therefore, the correct simplified equation equivalent to the given equation \( 15x - 5 + x = -47 \) is:
[tex]\[
\boxed{16x - 5 = -47}
\][/tex]
