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Solve for \( x \) \( 6(2 x+1)=18 \)

Ask by Newton Hanson. in the United States
Jan 24,2025

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\( x = 1 \)

Solución

To solve the equation \( 6(2x + 1) = 18 \) for \( x \), follow these steps: 1. **Distribute the 6** to both terms inside the parentheses: \[ 6 \times 2x + 6 \times 1 = 18 \] Simplifying: \[ 12x + 6 = 18 \] 2. **Subtract 6** from both sides of the equation to isolate the term with \( x \): \[ 12x + 6 - 6 = 18 - 6 \] Simplifying: \[ 12x = 12 \] 3. **Divide both sides** by 12 to solve for \( x \): \[ \frac{12x}{12} = \frac{12}{12} \] Simplifying: \[ x = 1 \] **Solution:** \( x = 1 \)

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The Deep Dive

To solve for \( x \), first distribute the 6 through the parentheses: \[ 6(2x + 1) = 18 \] This simplifies to: \[ 12x + 6 = 18 \] Next, subtract 6 from both sides: \[ 12x = 12 \] Now, divide both sides by 12: \[ x = 1 \] So, the solution is \( x = 1 \). Now let's have some additional fun facts! Did you know that algebra has its roots in ancient civilizations? The word "algebra" comes from the Arabic term "al-jabr," which was introduced by the mathematician Al-Khwarizmi in the 9th century. This was the beginning of a whole new approach to solving equations! In the real world, algebra is more than just numbers on a page; it helps us solve everyday problems! For example, businesses use algebra to calculate profits, determine pricing, or analyze trends. So, the next time you're balancing your budget or planning a trip, remember those simple equations can make big impacts in our lives!

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