Question

Solve the following equation and also check your result:
(3x − 8)(3x + 2) − (4x − 11)(2x + 1) = (x − 3)(x + 7)

Answer 1

\[(3x - 8)(3x + 2) - (4x - 11)(2x + 1) = (x - 3)(x + 7)\]
\[\text{ or }9 x^2 + 6x - 24x - 16 - 8 x^2 - 4x + 22x + 11 = x^2 + 7x - 3x - 21\]
\[\text{ or }x^2 - 5 = x^2 + 4x - 21\]
\[\text{ or }4x = - 5 + 21\]
\[\text{ or }x = \frac{16}{4} = 4\]
\[\text{ Thus, }x = 4\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ Substituting }x = 4 \text{ in the given equation, we get: }\]
\[\text{ L . H . S .} = (3 \times 4 - 8)(3 \times 4 + 2) - (4 \times 4 - 11)(2 \times 4 + 1) = 4 \times 14 - 5 \times 9 = 11\]
\[\text{ R . H . S .}= (4 - 3)(4 + 7) = 11\]
\[ \therefore\text{ L . H . S . = R . H . S . for } x = 4 .\]