which equation is an identity
X-3x=6x+5-8x
2(a-4)=4a-(2a+4)
-6x+3=-3(2x-1)
2(2a-1)=4(a-2)
The equation that is an identity is -6x+3=-3(2x-1).
To determine which equation is an identity, we need to simplify each equation and check if the simplified expressions are equal regardless of the values of the variables.
Let's go through each equation step by step:
1. X - 3x = 6x + 5 - 8x
Combining like terms on both sides:
X - 3x = -2x + 5
Rearranging terms:
X + 2x = 5
Combining like terms again:
3x = 5
Dividing both sides by 3:
x = 5/3
This equation depends on the value of x, so it is not an identity.
2. 2(a-4) = 4a - (2a+4)
Distributing the 2 on the left side:
2a - 8 = 4a - 2a - 4
Combining like terms on the right side:
2a - 8 = 2a - 4
Subtracting 2a from both sides:
-8 = -4
This equation is not true regardless of the values of a, so it is not an identity.
3. -6x + 3 = -3(2x - 1)
Distributing -3 on the right side:
-6x + 3 = -6x + 3
The variable terms and constant terms on both sides are equal, so this equation is an identity. It is always true regardless of the value of x.
4. 2(2a - 1) = 4(a - 2)
Distributing 2 on the left side:
4a - 2 = 4a - 8
The variable terms and constant terms on both sides are not equal, so this equation is not an identity. It is only true for specific values of a.
Therefore, the equation that is an identity is: -6x + 3 = -3(2x - 1).
To determine which equation is an identity, we need to simplify both sides of the equation and check if they are equal for all values of the variables. Let's go through each equation:
1. X-3x=6x+5-8x
To simplify this equation, combine like terms on both sides:
X - 3x = 6x - 3x + 5 - 8x
X - 3x = -5x + 5
This equation is not an identity because it can be solved for a specific value of x. For example, if x = 1, the equation becomes: 1 - 3(1) = -5(1) + 5, which is false.
2. 2(a-4) = 4a - (2a+4)
Let's distribute the 2 on the left side:
2(a) - 2(4) = 4a - 2a - 4
2a - 8 = 2a - 4
This equation is not an identity because the variable 'a' disappears when we simplify. It becomes 2a - 2a = -4 + 8, which simplifies to 0 = 4, which is false.
3. -6x + 3 = -3(2x - 1)
Simplify the right side of the equation by distributing -3:
-6x + 3 = -6x + 3
This equation is an identity because, after simplification, both sides of the equation are equal, irrespective of the value of 'x'.
4. 2(2a-1)=4(a-2)
Let's distribute 2 on the left side and 4 on the right side:
4a - 2 = 4a - 8
This equation is an identity because, after simplification, both sides of the equation are equal, irrespective of the value of 'a'.
In summary, the equations that are identities are:
-6x + 3 = -3(2x - 1)
2(2a-1) = 4(a-2)