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If z = (x-8)/(2x) then find x.

Question:

If {eq}\displaystyle \ z = \frac{x-8}{2x}\ {/eq} then find {eq}x {/eq}.

Basic Algebraic Expression:

{eq}\\ {/eq}

To get the value of the required variable {eq}\; x \; {/eq}, we will use some basic tools such as basic algebraic operations along with arithmetic operations. First of all, we will cross-multiply both the sides then we will put all the values of {eq}\; x \; {/eq} on one side and others on one side. Then we will go for the value of {eq}\; x \; {/eq}.

Answer and Explanation:

{eq}\\ {/eq}

{eq}\displaystyle \dfrac {z}{1} = \dfrac {x - 8}{2x} {/eq}

Now cross-multiply both the terms in the above expression:

{eq}\displaystyle z \times (2x) = x - 8 {/eq}

{eq}\displaystyle 2zx = x - 8 \\ 8 = x - 2zx \\ x (1 - 2z) = 8 {/eq}

Finally, the value of {eq}\; x \; {/eq} is given below:

{eq}\displaystyle \Longrightarrow \boxed {x = \dfrac {8}{1 - 2z}} {/eq}


Learn more about this topic:

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Basic Algebra: Rules, Equations & Examples

from SAT Subject Test Mathematics Level 2: Tutoring Solution

Chapter 4 / Lesson 10
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