Which equation is an identity?
(1 point)
Responses
11 – (2v + 3) = –2v – 8
11 – (2 v + 3) = –2 v – 8
5w + 8 – w = 6w – 2(w – 4)
5 w + 8 – w = 6 w – 2( w – 4)
7m – 2 = 8m + 4 – m
7 m – 2 = 8 m + 4 – m
8y + 9 = 8y – 3
The equation that is an identity is: 8y + 9 = 8y - 3.
Hey bot
Which equation has no solution?
(1 point)
Responses
5v + 3 = 5v – 5
5 v + 3 = 5 v – 5
2x – 4 = 2x + 7 – x
2 x – 4 = 2 x + 7 – x
2y + 5 – y = 2y – 3(y – 6)
2 y + 5 – y = 2 y – 3( y – 6)
7z + 9 = –7z – 6
The equation that is an identity is: 8y + 9 = 8y - 3.
To identify which equation is an identity, we need to find the equation that is true for all values of the variable(s) involved.
Let's analyze each equation:
1) 11 - (2v + 3) = -2v - 8
To simplify this equation, distribute the negative sign:
11 - 2v - 3 = -2v - 8
Combine like terms:
8 - 2v = -2v - 8
Observe that the variable terms (-2v) cancel each other out:
8 = -8
This equation is not true for any value of v. Therefore, it is not an identity.
2) 5w + 8 - w = 6w - 2(w - 4)
To simplify this equation, start by distributing the -2 inside the parentheses:
5w + 8 - w = 6w - 2w + 8
Combine like terms:
4w + 8 = 4w + 8
Observe that the variable terms (4w) are equal on both sides of the equation, and the constant terms (8) are also equal. This equation is true for all values of w. Therefore, it is an identity.
3) 7m - 2 = 8m + 4 - m
Combine like terms:
7m - 2 = 7m + 4
Observe that the variable terms (7m) are equal on both sides of the equation, but the constant terms (-2 and 4) are not equal. This equation is not true for any value of m. Therefore, it is not an identity.
4) 8y + 9 = 8y - 3
Observe that the variable terms (8y) are equal on both sides of the equation, but the constant terms (9 and -3) are not equal. This equation is not true for any value of y. Therefore, it is not an identity.
Out of the given equations, only equation 2) 5w + 8 - w = 6w - 2(w - 4) is an identity.