Question

solve the equation with step by step explaination​

Answer 1

Solution:-

$\rm \implies \: \dfrac{ {x}^{2} - (x + 2)(x + 3)}{7x + 1} = \dfrac{2}{3}$

$\rm \implies \: \dfrac{ {x}^{2} - ( {x}^{2} + 3x + 2x + 6) }{7x + 1} = \dfrac{2}{3}$

$\rm \implies \: \dfrac{ {x}^{2} - {x}^{2} - 5x - 6}{7x + 1} = \dfrac{2}{3}$

$\rm \implies \: \dfrac{ - 5x - 6}{7x + 1} = \dfrac{2}{3}$

Using cross multiplication method

$\rm \implies \: 3( - 5x - 6) = 2(7x + 1)$

$\rm \implies \: - 15x - 18 = 14x + 2$

$\rm \implies \: - 15x - 14x = 2 + 18$

$\implies \rm \: - 29x = 20$

$\rm \implies \: x = - \dfrac{20}{29}$

So answer is

$\rm \implies \: x = - \dfrac{20}{29}$

More about linear equation

Linear equation, statement that a first-degree polynomial—that is, the sum of a set of terms, each of which is the product of a constant and the first power of a variable—is equal to a constant.

A linear equation is an algebraic equation that forms a straight line when graphed. Each term is either a constant, or the product of a constant and a single variable.

Answer 2

$\underline{\orange{\bf Given :-}}$

$\implies\sf{\dfrac{x^{2} - (x + 2)(x + 3)}{7x + 1} = \dfrac{2}{3}}$

$\underline{\orange{\bf To \: Find :-}}$

$\implies\sf{Value \: of \: \boxed{\bf{x}}}$

$\underline{\orange{\bf Solution :-}}$

$\implies\sf{\dfrac{x^{2} - (x + 2)(x + 3)}{7x + 1} = \dfrac{2}{3}}$

$\implies\sf\dfrac{x^{2} - (x^{2} + 3x + 2x + 6)}{7x + 1} = \dfrac{2}{3}$

$\implies\sf\dfrac{x^{2} - (x^{2} + 5x + 6)}{7x + 1} = \dfrac{2}{3}$

$\implies\sf\dfrac{\cancel{x^{2}} \cancel{- x^{2}} - 5x - 6}{7x + 1} = \dfrac{2}{3}$

$\implies\sf\dfrac{- 5x - 6}{7x + 1} = \dfrac{2}{3}$

$\implies\sf - 15x - 18 = 14x + 2$

$\implies\sf - 15x - 14x = 2 + 18$

$\implies\sf - 29x = 20$

$\implies\underline{\boxed{\sf x = \dfrac{20}{- 29}}}$

Hence, the value of x is $\sf\dfrac{20}{- 29}$

______________________________

Additional Information :-

1) + × + = +

☆ Example :-

• 5x × 2x = 10x²

2) + × - = -

☆ Example :-

• 5x × (- 2x) = - 10x²

3) - × - = +

☆ Example :-

• (- 5x) × (- 2x) = 10x²

______________________________