Question

question
solve for all values of $x$:
$-dfrac{4x}{x+7}+3=dfrac{6}{x+7}$
answer attempt 1 out of 2
additional solution no solution
$x =$

Explanation:

Step1: Eliminate denominator

Multiply all terms by $x+7$ (where $x
eq -7$):
$$-\frac{4x}{x+7}(x+7) + 3(x+7) = \frac{6}{x+7}(x+7)$$
Simplify to get:
$$-4x + 3(x+7) = 6$$

Step2: Expand and simplify left side

Expand the bracket and combine like terms:
$$-4x + 3x + 21 = 6$$
$$-x + 21 = 6$$

Step3: Isolate the variable term

Subtract 21 from both sides:
$$-x = 6 - 21$$
$$-x = -15$$

Step4: Solve for x

Multiply both sides by -1:
$$x = 15$$

Step5: Verify the solution

Check if $x=15$ makes the original denominator zero: $15+7=22
eq 0$, so it is valid.

Answer:

$x=15$