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Solve for \( f \). \( -f+2+4 f=8-3 f \) \( f= \) I I Related content

Ask by Mckenzie Willis. in the United States
Jan 25,2025

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\( f = 1 \)

Solución

Let's solve the equation step by step to find the value of \( f \): \[ -f + 2 + 4f = 8 - 3f \] 1. **Combine like terms on the left side:** \[ (-f + 4f) + 2 = 8 - 3f \] \[ 3f + 2 = 8 - 3f \] 2. **Add \( 3f \) to both sides to get all \( f \) terms on one side:** \[ 3f + 3f + 2 = 8 \] \[ 6f + 2 = 8 \] 3. **Subtract 2 from both sides to isolate the term with \( f \):** \[ 6f = 8 - 2 \] \[ 6f = 6 \] 4. **Divide both sides by 6 to solve for \( f \):** \[ f = \frac{6}{6} \] \[ f = 1 \] **Answer:** \( f = 1 \)

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Bonus Knowledge

To solve for \( f \), let's first simplify the equation: \[ -f + 4f + 3f = 8 - 2 \] This combines like terms: \[ 6f = 6 \] Now, divide both sides by 6: \[ f = 1 \] So, \( f = 1 \). For those who enjoy historical tidbits about algebra, did you know that the word "algebra" comes from the Arabic term "al-jabr"? This word was first popularized by the mathematician Al-Khwarizmi in the 9th century! Algebra has its roots in ancient civilizations, where it was used for solving various problems related to trade and land measurement. Now, if you're solving equations, remember that one common mistake is forgetting to apply the same operation to both sides of the equation. Always keep the equation balanced, and don’t hesitate to check your work by plugging your answer back into the original equation!

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