What is the answer to a(3x-4)+b(5x-7)=2a+3b ?

The answer to a(3x-4)+b(5x-7)=2a+3b is x=2;\quad a\ne-(5b)/3

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a(3x-4)+b(5x-7)=2a+3b

a (3 x - 4) + b (5 x - 7) = 2 a + 3 b

x = 2; a \neq = - \frac{5 b}{3}

Solution steps

a (3 x - 4) + b (5 x - 7) = 2 a + 3 b

Expand

a (3 x - 4) : 3 a x - 4 a

3 a x - 4 a + b (5 x - 7) = 2 a + 3 b

Expand

b (5 x - 7) : 5 b x - 7 b

3 a x - 4 a + 5 b x - 7 b = 2 a + 3 b

Move

4 a

to the right side

3 a x + 5 b x - 7 b = 6 a + 3 b

Move

7 b

to the right side

3 a x + 5 b x = 6 a + 10 b

Factor

3 a x + 5 b x : x (3 a + 5 b)

x (3 a + 5 b) = 6 a + 10 b

Divide both sides by

3 a + 5 b; a \neq = - \frac{5 b}{3}

x = 2; a \neq = - \frac{5 b}{3}

p, 6 p - 12 q = 18

- 6 (4 x + 1) + 7 (3 x + 1) = 90

p, p + 2 q = 5

t, \frac{5 p - 3 t}{4} = a - 2 t

p, 3 p - 6 q = 9

What is the answer to a(3x-4)+b(5x-7)=2a+3b ?
The answer to a(3x-4)+b(5x-7)=2a+3b is x=2;\quad a\ne-(5b)/3