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QuestionSolve for mm in the equation 4m−8=82\frac{4}{m-8}=\frac{8}{2}.

Studdy Solution

STEP 1

Assumptions1. The equation is 4m−8=8\frac{4}{m-8}=\frac{8}{} . We are solving for mm

STEP 2

First, simplify the right side of the equation.
82=4\frac{8}{2} =4So, the equation becomes4m−8=4\frac{4}{m-8} =4

STEP 3

To isolate mm, we can first get rid of the fraction by multiplying both sides of the equation by (m−8)(m-8).
(m−8)⋅m−8=⋅(m−8)(m-8) \cdot \frac{}{m-8} = \cdot (m-8)

STEP 4

implify the left side of the equation, the (m−8)(m-8) cancels out.
4=4⋅(m−8)4 =4 \cdot (m-8)

STEP 5

Now, distribute the4 on the right side of the equation.
4=4m−324 =4m -32

STEP 6

Next, we isolate mm by adding32 to both sides of the equation.
4+32=4m−32+324 +32 =4m -32 +32

STEP 7

implify both sides of the equation.
36=4m36 =4m

STEP 8

Finally, divide both sides of the equation by4 to solve for mm.
364=4m4\frac{36}{4} = \frac{4m}{4}

STEP 9

implify both sides of the equation to find the value of mm.
m=364=9m = \frac{36}{4} =9So, the solution to the equation is m=9m =9.

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