Question

Solve the equation. Then determine whether the equation is an​ identity, a conditional​ equation, or an inconsistent equation.
3xplus24equals8​(xplus3​)minus5x

Answer 1

To solve the equation \( 3x + 24 = 8(x + 3) - 5x \), let's first simplify the right-hand side of the equation.

1. Distribute \( 8 \) on the right-hand side:
\[
8(x + 3) = 8x + 24
\]
So, the equation becomes:
\[
3x + 24 = 8x + 24 - 5x
\]

2. Simplify the right-hand side:
\[
8x - 5x + 24 = 3x + 24
\]
This simplifies to:
\[
3x + 24 = 3x + 24
\]

Now, we can see that both sides of the equation are equal. This indicates that the equation is true for all values of \( x \).

#### Conclusion:
Since the equation holds for all \( x \), it is an **identity**.