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5. a. Solve: \( \frac{1}{2} x+8 \leq 10 \)

Ask by Savage Thornton. in the United States
Jan 22,2025

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\( x \leq 4 \)

Solución

To solve the inequality: \[ \frac{1}{2} x + 8 \leq 10 \] Follow these steps: ### Step 1: Subtract 8 from both sides \[ \frac{1}{2} x + 8 - 8 \leq 10 - 8 \] Simplifying: \[ \frac{1}{2} x \leq 2 \] ### Step 2: Multiply both sides by 2 to isolate \( x \) Since you're multiplying by a positive number, the direction of the inequality remains the same. \[ 2 \times \left( \frac{1}{2} x \right) \leq 2 \times 2 \] Simplifying: \[ x \leq 4 \] ### **Solution** \[ x \leq 4 \] This means that any real number \( x \) that is **4 or less** satisfies the original inequality.

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Bonus Knowledge

To solve the inequality \( \frac{1}{2} x + 8 \leq 10 \), first, you would want to isolate \( x \). Start by subtracting 8 from both sides: \[ \frac{1}{2} x \leq 2 \] Next, multiply both sides by 2 to eliminate the fraction: \[ x \leq 4 \] So, the solution to the inequality is \( x \leq 4 \). Remember, when solving inequalities, if you multiply or divide by a negative number, you have to flip the inequality sign. That's a common pitfall! Stay mindful of that, and you'll breeze through each problem with confidence!

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