# If |2/x| = y does 1 = |x/2|y ?

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In summary, to solve the equation |2/x| = y, you need to isolate the absolute value on one side and consider both positive and negative solutions. This equation represents a relationship between the absolute value of a number and a variable, and can be graphed as a V-shaped curve. The equation 1 = |x/2|y has the same solution set as the original equation, and the equation |2/x| = y can be applied in real life situations where there is a known proportional relationship between two quantities.
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If |2/x| = y does 1 = |x/2|y ?

Yes, as long as a is not 0 (and |2/x| cannot be 0 for any x) a= y is the same as 1= y/a= (1/a)x. Taking a= |2/x|, 1/a= |x/2|.

## 1. How do you solve the equation |2/x| = y?

To solve this equation, you need to isolate the absolute value on one side of the equation. You can do this by dividing both sides by 2, which will give you |x| = 2y. Then, you can remove the absolute value by considering both the positive and negative solutions, giving you x = 2y or x = -2y.

## 2. What does the equation |2/x| = y represent?

This equation represents a relationship between the absolute value of a number and a variable. It is saying that the absolute value of 2 divided by x will always equal y. This can be seen as a function where y is the output and x is the input.

## 3. How do you graph the equation |2/x| = y?

To graph this equation, you can first plot the points where x = 2y and x = -2y. Then, you can draw a line connecting these points. The graph will be a V-shaped curve, with the vertex at the origin (0,0).

## 4. How does the equation 1 = |x/2|y relate to the original equation |2/x| = y?

The equations are related in that they have the same solution set. When solving the original equation, you get two possible solutions: x = 2y or x = -2y. When substituting these values into the second equation, you will get 1 for both solutions, showing that they are equivalent.

## 5. How can the equation |2/x| = y be applied in real life?

This equation can be applied in situations where there is a known relationship between two quantities, and the absolute value of one quantity is proportional to the other quantity. For example, in physics, the speed of an object can be represented by |2/x|, where x is the distance traveled and y is the time taken. In this case, y would represent the speed of the object.

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