Determine whether the equation is an identity or whether it has no solution. 4(a - 6) = 8a - (4a + 24) The equation has no solution is an identity
To determine whether the equation has no solution or is an identity, we need to simplify both sides of the equation and see if the resulting expressions are equal.
Starting on the left side:
4(a - 6) = 4a - 24
And on the right side:
8a - (4a + 24) = 8a - 4a - 24 = 4a - 24
Therefore, the equation becomes:
4a - 24 = 4a - 24
As we can see, both sides of the equation are identical. Therefore, this equation is an identity.
To determine whether the equation 4(a - 6) = 8a - (4a + 24) is an identity or has no solution, let's simplify the equation step by step.
1. Start by simplifying both sides of the equation:
On the left side, we distribute the 4:
4(a - 6) = 4a - 24
On the right side, we simplify the inner parentheses:
8a - (4a + 24) = 8a - 4a - 24
Since there is no operation between the -4a and -24, we can combine them:
8a - 4a - 24 = 4a - 24
2. Now, compare the simplified equation:
4(a - 6) = 8a - (4a + 24) simplifies to:
4a - 24 = 4a - 24
Both sides of the equation are exactly the same.
3. Thus, we can conclude that the equation is an identity.
Therefore, the equation 4(a - 6) = 8a - (4a + 24) is an identity.