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In the expression A(x+5)+2(-Bx+2), the coefficient of x is 17 and the constant term is 359. What is the value of A-B?

Note by Eka Kurniawan
3 years, 7 months ago

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A(x+5) = Ax + 5A

2(-Bx+2) = -2Bx + 4

I A - 2B = 17 (coefficient of x)

II 5A + 4 = 359 (the constant term is 359)

II 5A = 355

A = 71

So.. I 71 - 2B = 17

2B = 54

B = 27

A - B = 71 - 27 = 44

Felipe Magalhães - 3 years, 7 months ago

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ooo, okay! now I understand what the question means

Eka Kurniawan - 3 years, 6 months ago

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\( A(x+5) + 2(-Bx + 2) \)

Opening the brackets, we get,

\( Ax + 5A - 2Bx + 4 \)

Grouping Like terms together,

\( (A - 2B)x + (5A + 4) \)

Now, by the question,

\( A - 2B = 17, 5A + 4 = 359 \)

Solving the second equation,

\( 5A = 355 \rightarrow A = 71 \)

Putting the value of A in the first equation

\( 71 - 2B = 17 \rightarrow 54 = 2B \rightarrow B = 27 \)

To find, \( A - B = 71 - 27 = \boxed{44} \)

Siddhartha Srivastava - 3 years, 7 months ago

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