Solve for all values of x. (3x)/(11)=(3)/(11 x) Answer: x=

Identify Proportion Equation: First, we need to identify that the equation is a proportion where two ratios are equal. We can cross-multiply to find the values of x. Cross-multiplication will give us 3x * 11x = 3 * 11.Cross-Multiply to Find x: Perform the multiplication on both sides of the equation. On the left side, we multiply 3x by 11x, which gives us 33x^2. On the right side, we multiply 3 by 11, which gives us 33. So, the equation becomes 33x^2 = 33.Perform Multiplication: Next, we can simplify the equation by dividing both sides by 33 to isolate x^2. When we divide 33x^2 by 33, we get x^2. When we divide 33 by 33, we get 1. So, the equation simplifies to x^2 = 1.Simplify Equation: To find the values of x, we take the square root of both sides of the equation. The square root of x^2 is x, and the square root of 1 is 1. However, we must remember that taking the square root of a number yields both a positive and a negative solution. So, x can be either 1 or -1.

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Algebra 2

Simplify variable expressions using properties

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Q. Solve for all values of

x

\newline

\frac{3 x}{11}=\frac{3}{11 x}

\newline

Answer:

x=

Identify Proportion Equation: First, we need to identify that the equation is a proportion where two ratios are equal. We can cross-multiply to find the values of $x$ . Cross-multiplication will give us $3x \times 11x = 3 \times 11$ .
Cross-Multiply to Find $x$ : Perform the multiplication on both sides of the equation. On the left side, we multiply $3x$ by $11x$ , which gives us $33x^2$ . On the right side, we multiply $3$ by $11$ , which gives us $33$ . So, the equation becomes $33x^2 = 33$ .
Perform Multiplication: Next, we can simplify the equation by dividing both sides by $33$ to isolate $x^2$ . When we divide $33x^2$ by $33$ , we get $x^2$ . When we divide $33$ by $33$ , we get $1$ . So, the equation simplifies to $x^2 = 1$ .
Simplify Equation: To find the values of $x$ , we take the square root of both sides of the equation. The square root of $x^2$ is $x$ , and the square root of $1$ is $1$ . However, we must remember that taking the square root of a number yields both a positive and a negative solution. $\newline$ So, $x$ can be either $1$ or $-1$ .