What is the answer to 2x+3=a(x-2)+b(x-1) ?

The answer to 2x+3=a(x-2)+b(x-1) is x=(-2a-b-3)/(2-a-b);\quad a\ne-b+2

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2x+3=a(x-2)+b(x-1)

2 x + 3 = a (x - 2) + b (x - 1)

x = \frac{- 2 a - b - 3}{2 - a - b}; a \neq = - b + 2

Solution steps

2 x + 3 = a (x - 2) + b (x - 1)

Expand

a (x - 2) : a x - 2 a

2 x + 3 = a x - 2 a + b (x - 1)

Expand

b (x - 1) : b x - b

2 x + 3 = a x - 2 a + b x - b

Move

3

to the right side

2 x = a x - 2 a + b x - b - 3

Subtract

a x + b x

from both sides

2 x - (a x + b x) = a x - 2 a + b x - b - 3 - (a x + b x)

Simplify

2 x - a x - b x = - 2 a - b - 3

Factor

2 x - a x - b x : x (2 - a - b)

x (2 - a - b) = - 2 a - b - 3

Divide both sides by

2 - a - b; a \neq = - b + 2

x = \frac{- 2 a - b - 3}{2 - a - b}; a \neq = - b + 2

x, - 2 x + y + z = 1

10 + (- 5) c = 75

i (x) = 20, 0 - \frac{3630}{x} + 1 c (x) = 400 + 10 x + x^{2}

1.8 x + 12.4 = 25

0.003 (k - 4) + 0.08 (k - 7) = 1

What is the answer to 2x+3=a(x-2)+b(x-1) ?
The answer to 2x+3=a(x-2)+b(x-1) is x=(-2a-b-3)/(2-a-b);\quad a\ne-b+2