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Solve the following equation for X. Remember to balance the equation?

How to solve the following equation?

  • I am not sure how to solver the following equation for B and A explanation would be much appreciated. Thank you Solve the equation for A and B. A(x - 2) + B(x + 1) = x

  • Answer:

    i will tell u a shortcut since this must be true for all values of x put x=2??Y A will vanish from eqn leaving behind B A(2 - 2) + B(2 + 1) = 2 0+3B=2 B=2/3 similarly put x= -1 ??Y B will vanish from eqn leaving behind A A(-1 - 2) + B(-1 + 1) = -1 -3A + 0 = -1 A=1/3 else simplify equate coefficients of A and B ....simplified eqn A(x - 2) + B(x + 1) = x (A+B)x + (B-2A) = x so A+B=1 B-2A=0 just solve these both

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LHS = A (x-2) + B (x+1) = Ax -2A +Bx + B so we have (A+B)x + (B-2A) = x setting the co efficients equal, A+B=1 and B-2A=0 Solving this system yields A=1/3 and B=2/3

Michael Ponds

In order to find numerical values for 3 unknowns would require 3 equations. So, we are going to "solve for" each variable as though they are formulas. A(x - 2) + B(x + 1) = x B(x + 1) = x - A(x - 2) isolate the "B" term B = [ x - A(x - 2) ] / (x+1) isolate "B" This is "solved for B" A(x - 2) + B(x + 1) = x A(x - 2) = x - B(x + 1) isolate the "A" term A = [ x - B(x + 1) ] / (x-2) isolate "A" This is "solved for A"

bedbye

Solving for A: A = [x - B(x+1)]/(x-2) To solve: - subtract B(x+1) on both sides of the equals sign: - you are left with: A(x-2) = x - B(x+1) - Divide both sides by (x-2) - you are left with A = [x - B(x+1)]/(x-2) Solving for B: B = [x - A(x-2)]/(x+1) To solve: - subtract A(x-2) on both sides of the equals sign: - you are left with: B(x+1) = x - A(x-2) - Divide both sides by (x+1) - you are left with B = [x - A(x-2)]/(x+1)

David

A(x - 2) + B(x + 1) = x A(x - 2) = x - B(x + 1) A = (x - B(x - 1))/(x - 2) B(x + 1) = x - A(x - 2) B = (x - A(x - 2))/(x + 1)

Battleaxe

yes

Gateau

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