Question

Solve the following equation, to find the value of x :
1. (x + 5) (x + 6) = (x - 7) (x - 8)
2. (x + 1) (x + 2) = (x - 3) (x - 4)​

Answer 1

1) (x + 5) ( x + 6) = ( x - 7) (x - 8)

$\sf \: (x + 5)(x + 6) = (x - 7)(x - 8)$

${x}^{2} + 6x + 5x + 30 = {x}^{2} - 8x - 7x + 56$

Cancel x² from both sides.

$6x + 5x + 30 = - 8x - 7x + 56$

$11x + 30 = - 15x + 56$

$\sf \implies \: 11x + 15x = 56 - 30$

$\sf \implies \: 26x = 26$

$\sf \implies \: x = 1$

2) (x + 1) (x + 2 ) = (x -3) (x -4)

${x}^{2} + 2x + x + 2 = {x}^{2} - 4x - 3x + 12$

Cancel x² from both sides.

$2x + x + 2 = - 4x - 3x + 12$

Collect like terms.

$3x + 2 = - 7x + 12$

$3x + 7x = 12 - 2$

$10x = 10$

Divide both sides by 10.

$\sf \implies \: x = 1$

Answer 2

Solution :

1. (x + 5) (x + 6) = (x - 7) (x - 8)

➜ (x + 5) (x + 6) = (x - 7) (x - 8)

➜ x (x + 5) + 6 (x + 5) = x (x - 7) - 8 (x - 7)

➜ x² + 5x + 6x + 30 = x² - 7x - 8x + 56

➜ x² + 11x + 30 = x² - 15x + 56

➜ x² - x² + 11x + 15x + 30 - 56 = 0

➜ 26x - 26= 0

➜ 26x = 26

➜ x = 26/26

➜ x = 1

2. (x + 1) (x + 2) = (x - 3) (x - 4)

➜ (x + 1) (x + 2) = (x - 3) (x - 4)

➜ x (x + 2) + 1 (x + 2) = x (x - 4) - 3 (x - 4)

➜ x² + 2x + x + 2 = x² - 4x - 3x + 12

➜ x² + 2x + x + 2 - x² + 4x + 3x - 12 = 0

➜ x² - x² + 2x + 4x + x + 3x + 2 - 12 = 0

➜ 6x + 4x - 10 = 0

➜ 10x - 10 = 0

➜ 10x = 10

➜ x = 10/10

➜ x = 1

Answer : Hence, in both the equations, the value of x is 1.