Solve for x. 2-(6)/(x)=(1)/(2) Answer: x=

Isolate x term: Isolate the term containing x. To isolate the term with x, we need to move the constant term on the left side of the equation to the right side. We do this by adding (6/x) to both sides of the equation. 2 - (6/x) + (6/x) = (1/2) + (6/x) This simplifies to: 2 = (1/2) + (6/x)Subtract constant: Subtract (1/2) from both sides to further isolate the term with x. 2 - (1/2) = (1/2) - (1/2) + (6/x) This simplifies to: (4/2) - (1/2) = (6/x) 3/2 = (6/x)Cross-multiply for x: Cross-multiply to solve for x. We have the equation in the form of a fraction equal to another fraction, so we can cross-multiply to find x. (3/2) * x = 6 * 1 This simplifies to: (3x/2) = 6Multiply by 2: Multiply both sides by 2 to solve for x. (3x/2) * 2 = 6 * 2 This simplifies to: 3x = 12Divide by 3: Divide both sides by 3 to find the value of x. 3x / 3 = 12 / 3 This simplifies to: x = 4

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Math Problems

Algebra 2

Simplify variable expressions using properties

Full solution

Q. Solve for

x

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2-\frac{6}{x}=\frac{1}{2}

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Answer:

x=

Isolate x term: Isolate the term containing x. $\newline$ To isolate the term with x, we need to move the constant term on the left side of the equation to the right side. We do this by adding $(6/x)$ to both sides of the equation. $\newline$ $2 - (6/x) + (6/x) = (1/2) + (6/x)$ $\newline$ This simplifies to: $\newline$ $2 = (1/2) + (6/x)$
Subtract constant: Subtract $(1/2)$ from both sides to further isolate the term with $x$ . $2 - (1/2) = (1/2) - (1/2) + (6/x)$ This simplifies to: $(4/2) - (1/2) = (6/x)$ $3/2 = (6/x)$
Cross-multiply for x: Cross-multiply to solve for x. $\newline$ We have the equation in the form of a fraction equal to another fraction, so we can cross-multiply to find $x$ . $\newline$ $(\frac{3}{2}) \cdot x = 6 \cdot 1$ $\newline$ This simplifies to: $\newline$ $(\frac{3x}{2}) = 6$
Multiply by $2$ : Multiply both sides by $2$ to solve for $x$ . $\left(\frac{3x}{2}\right) \times 2 = 6 \times 2$ This simplifies to: $3x = 12$
Divide by $3$ : Divide both sides by $3$ to find the value of x. $\newline$ $\frac{3x}{3} = \frac{12}{3}$ $\newline$ This simplifies to: $\newline$ $x = 4$