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.

Step-by-step 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

The answer is 24.50