Question

question solve for all values of x. $2x+\frac{7}{x + 6}=3x$ answer attempt 1 out of 2 additional solution no solution $x =$ submit answer

Explanation:

Step1: Move terms to simplify

Subtract $2x$ from both sides: $\frac{7}{x + 6}=3x - 2x=x$.

Step2: Cross - multiply

We get $7=x(x + 6)$.

Step3: Expand and form quadratic equation

Expand the right side: $7=x^{2}+6x$, which can be rewritten as $x^{2}+6x - 7 = 0$.

Step4: Factor the quadratic equation

Factor $x^{2}+6x - 7$ as $(x + 7)(x - 1)=0$.

Step5: Solve for x

Set each factor equal to zero: $x+7 = 0$ gives $x=-7$; $x - 1=0$ gives $x = 1$.

Answer:

$x=-7,1$