Which equation is an identity?

An equation is an identity if both sides of the equation are equal to one another. For example, the equation x + 1 = x + 1 is an identity because x + 1 obviously is equal to x + 1. Now, we need to simplify each of these equations and see which one is an identity. Let's start with A.

8 - (6v + 7) = -6v - 1

8 - 7 - 6v = -6v - 1

-6v + 1 = -6v -1

Since this is not true, a is not the answer. Now onto b.

6m - 6 = 7m + 9 - m

6m - 6 = 6m + 9

Since this is obviously not the case, we move onto c.

3w + 8 - w = 4w -2(w - 4)

2w + 8 = 4w - 2w + 8

2w + 8 = 2w + 8

Since the two sides of the equation are equal, that means that the answer is C.

MrRoyal MrRoyal · Answer 2 · 2021-09-28T13:16:34+02:00

Both sides of an identity equation are equal.

[tex](c)\ 3w + 8-w = 4w -2(w - 4)[/tex] is an identity equation

First, we test the options until one of them is true

[tex](a)\ 8 - (6v + 7) = -6v -1[/tex]

Open brackets

[tex]8 - 6v - 7 = -6v -1[/tex]

Collect like terms

[tex]- 6v+8 - 7 = -6v -1[/tex]

[tex]- 6v+1 = -6v -1[/tex]

Add 6v to both sides

[tex]1= -1[/tex]

Both sides are not equal.

Hence, (a) is not an identity equation

[tex](b)\ 6m - 6 = 7m +9 - m[/tex]

Collect like terms

[tex]6m - 6 = 7m - m+9[/tex]

[tex]6m - 6 = 6m+9[/tex]

Subtract 6m from both sides

[tex]- 6 = 9[/tex]

Both sides are not equal.

Hence, (b) is not an identity equation

[tex](c)\ 3w + 8-w = 4w -2(w - 4)[/tex]

Open brackets

[tex]3w + 8-w = 4w -2w + 8[/tex]

Collect like terms

[tex]3w -w+ 8 = 4w -2w + 8\\[/tex]

Evaluate like terms

[tex]2w+ 8 = 2w + 8[/tex]

Both sides are equal.

Hence, (c) is an identity equation

Read more about identity equations at:

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