Question

question
solve for all values of x.
\\(\frac{4}{x} = \frac{4x}{9}\\)
answer attempt 1 out of 2
additional solution no solution

Explanation:

Step1: Cross-multiply to eliminate denominators

$4 \times 9 = 4x \times x$

Step2: Simplify both sides of the equation

$36 = 4x^2$

Step3: Divide by 4 to isolate $x^2$

$x^2 = \frac{36}{4} = 9$

Step4: Solve for $x$ by taking square roots

$x = \pm\sqrt{9} = \pm 3$

Step5: Verify valid solutions (x≠0)

Both $x=3$ and $x=-3$ are non-zero, so they are valid.

Answer:

$x = 3$ and $x = -3$