Is the equation identity or conditional? 3(x+2)=3x+6
3(x+4)=3x+4
3(x+2) = 3*x + 3*2 = 3x+6
an identity
3(x+4) = 3*x + 3*4 = 3x+12 ≠ 3x+4
not only not an identity, but not even conditional. There is no value of x which makes it true!
To determine whether an equation is an identity or conditional, we need to compare the left-hand side (LHS) and right-hand side (RHS) of the equation.
Let's start with the first equation: 3(x+2) = 3x+6.
To solve this equation, we will simplify both sides of the equation by distributing the 3 on the left-hand side:
3x + 6 = 3x + 6.
Now, let's analyze the equation. Notice that the LHS and RHS of the equation are identical. This means that no matter what value we choose for x, the equation will always be true. Hence, the equation is an identity.
Now, let's move on to the second equation: 3(x+4) = 3x + 4.
Again, we will simplify both sides of the equation by distributing the 3 on the left-hand side:
3x + 12 = 3x + 4.
Now, upon closer inspection, we can see that the LHS (3x + 12) does not equal the RHS (3x + 4). This means that there is no value of x that can simultaneously satisfy both sides of the equation. As a result, the equation is conditional.
In summary:
- The equation 3(x+2) = 3x+6 is an identity since the LHS and RHS are identical.
- The equation 3(x+4) = 3x+4 is conditional since the LHS and RHS are not equal.