Question

11 multiple choice 1 point
what is the solution of $\frac{5}{x}+\frac{3}{2}=\frac{8}{4x}$
no real solution
8
4
-2
clear my selection
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Explanation:

Step1: Eliminate denominators

Multiply all terms by $4x$ (the least common multiple of $x, 2, 4x$):
$$4x \cdot \frac{5}{x} + 4x \cdot \frac{3}{2} = 4x \cdot \frac{8}{4x}$$
Simplify each term:
$$20 + 6x = 8$$

Step2: Isolate the variable term

Subtract 20 from both sides:
$$6x = 8 - 20$$
$$6x = -12$$

Step3: Solve for x

Divide both sides by 6:
$$x = \frac{-12}{6} = -2$$

Step4: Verify the solution

Substitute $x=-2$ back into the original equation:
$$\frac{5}{-2} + \frac{3}{2} = \frac{8}{4(-2)}$$
$$\frac{-5 + 3}{2} = \frac{8}{-8}$$
$$\frac{-2}{2} = -1$$
$$-1 = -1$$
The solution is valid.

Answer:

-2