Solve for all values of x. (x)/( 10)=(8)/(5x) Answer: x=

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Solve for all values of  x.  (x)/( 10)=(8)/(5x) Answer:  x=

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Eliminate Fractions: First, we need to eliminate the fractions by cross-multiplying to get rid of the denominators. This will give us a simpler equation to work with. Cross-multiplication gives us: x * 5x = 10 * 8Simplify Equation: Next, we simplify the equation by performing the multiplication on both sides. This results in: 5x^2 = 80Set to Zero: Now, we want to set the equation to zero to solve for x by moving all terms to one side. Subtract 80 from both sides to get: 5x^2 - 80 = 0Factor Quadratic: To solve the quadratic equation, we can factor it if possible. Let's see if the quadratic can be factored easily. Factoring gives us: 5(x^2 - 16) = 5(x + 4)(x - 4) = 0Apply Zero Product Property: Now, we apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. Setting each factor equal to zero gives us two equations: x + 4 = 0 and x - 4 = 0Solve for x: Solve each equation for x. For x + 4 = 0, subtracting 4 from both sides gives us x = -4. For x - 4 = 0, adding 4 to both sides gives us x = 4.

Solve for all values of $x$ . $\newline$ $\frac{x}{10}=\frac{8}{5 x}$ $\newline$ Answer: $x=$

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Solve for all values of $x$ . $\newline$ $\frac{x}{10}=\frac{8}{5 x}$ $\newline$ Answer: $x=$