What is the answer to ((2x-a))/b =((2x-b))/a ?

The answer to ((2x-a))/b =((2x-b))/a is x=(a+b)/2 ;\quad b\ne 0,a\ne 0,a\ne b

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

\frac{( 2 x - a )}{b} = \frac{( 2 x - b )}{a}

x = \frac{a + b}{2}; b \neq = 0, a \neq = 0, a \neq = b

Solution steps

\frac{( 2 x - a )}{b} = \frac{( 2 x - b )}{a}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

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

Expand

(2 x - a) a : 2 a x - a^{2}

Expand

b (2 x - b) : 2 b x - b^{2}

2 a x - a^{2} = 2 b x - b^{2}; b \neq = 0, a \neq = 0

Move

a^{2}

to the right side

2 a x = 2 b x - b^{2} + a^{2}; b \neq = 0, a \neq = 0

Move

2 b x

to the left side

2 a x - 2 b x = - b^{2} + a^{2}; b \neq = 0, a \neq = 0

Factor

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

2 x (a - b) = - b^{2} + a^{2}; b \neq = 0, a \neq = 0

Divide both sides by

2 (a - b); b \neq = 0, a \neq = 0, a \neq = b

x = \frac{a + b}{2}; b \neq = 0, a \neq = 0, a \neq = b

2 x + 2 b = a

4 = 0.3 q + 2

x, 3 x + 2 y = 29

10 (1.5)^{3} x = 80

m, 300 n = 0.8 m

What is the answer to ((2x-a))/b =((2x-b))/a ?
The answer to ((2x-a))/b =((2x-b))/a is x=(a+b)/2 ;\quad b\ne 0,a\ne 0,a\ne b