Answer:
w = 12
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle{\dfrac{w-2}{4} = \dfrac{2w+1}{10}}[/tex]
First, clear out the denominators by multiplying both sides by LCM. In this scenario, our LCM is 40. Thus, multiply both sides by 40:
[tex]\displaystyle{\dfrac{w-2}{4} \cdot 40= \dfrac{2w+1}{10} \cdot 40}[/tex]
Simplify the expressions/equations:
[tex]\displaystyle{(w-2)\cdot 10= (2w+1)\cdot 4}\\\\\displaystyle{10w-20= 8w+4}[/tex]
Isolate w-variable:
[tex]\displaystyle{10w-20= 8w+4}\\\\\displaystyle{10w-8w=4+20}\\\\\displaystyle{2w=24}\\\\\displaystyle{w=12}[/tex]
Hence, the solution is w = 12
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