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\( 5(x-4)-25 \% \) of \( (x-5)=20 \)

Ask by Garrett Davey. in India
Jan 22,2025

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\( x = \frac{155}{19} \approx 8.16 \)

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Mind Expander

To solve the equation \( 5(x-4)-25\% \) of \( (x-5)=20 \), let's break it down step by step. 1. First, we can express \( 25\% \) as a decimal, which is \( 0.25 \). Therefore, \( 25\% \) of \( (x-5) \) can be written as \( 0.25(x-5) \). 2. Now, substituting back into the equation gives us: \[ 5(x-4) - 0.25(x-5) = 20 \] 3. Next, distribute the terms: \[ 5x - 20 - 0.25x + 1.25 = 20 \] 4. Combine like terms: \[ (5x - 0.25x) - 20 + 1.25 = 20 \implies 4.75x - 18.75 = 20 \] 5. Now, isolate \( x \): \[ 4.75x = 20 + 18.75 \implies 4.75x = 38.75 \] 6. Finally, divide by \( 4.75 \): \[ x = \frac{38.75}{4.75} = 8.16 \] Thus, the solution to the equation is approximately \( x \approx 8.16 \).

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