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Chapter 2: Problem 113

(a) Solve the equation \(y=z / x\) for \(x\). (b) Solve the equation \(y=z / 2 x\) for \(x\).

Short Answer

Expert verified
(a) \( x = \frac{z}{y} \) (b) \( x = \frac{z}{2y} \)

Step by step solution

01

(a) Step 1: Rearrange the equation to isolate x in terms of y and z

We are given the equation: \( y = \frac{z}{x} \) To isolate x, we can multiply both sides of the equation by x, which gives: \( xy = z \)
02

(a) Step 2: Solve for x in terms of y and z

Now we need to continue to manipulate this equation to solve for x. Since y is being multiplied by x, we can divide both sides of the equation by y, resulting in: \( x = \frac{z}{y} \)
03

(b) Step 1: Rearrange the equation to isolate x in terms of y and z

We are given the equation: \( y= \frac{z}{2x} \) To isolate x, we can multiply both sides of the equation by 2x, which gives: \( 2xy = z \)
04

(b) Step 2: Solve for x in terms of y and z

Now we need to continue to manipulate this equation to solve for x. Since 2y is being multiplied by x, we can divide both sides of the equation by 2y, resulting in: \( x = \frac{z}{2y} \)

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