Question

12

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CCSS Persevere with Problems Suppose A and B represent linear expressions.
If A + B = 2x – 2 and A - B = 4x – 8, find A and B.

Answer 1

A = 3x – 5 and B = 3 – x

Explanation:

The given linear expressions are:

A + B = 2x – 2 ...... (1)

and A - B = 4x – 8 ...... (2)

To find, the value of A and B = ?

Adding equations (1) and (2), we get

A + B + A - B = 2x – 2 + 4x – 8

⇒ A + A = 6x – 10

⇒ 2A = 2(3x – 5)

⇒ A = 3x – 5

Putting the value of A in equation (1), we get

3x – 5 + B = 2x – 2

⇒ B = 2x – 2 - 3x + 5

⇒ B = 3 – x

Thus, A = 3x – 5 and B = 3 – x