Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x \leq 4 \)
Solution
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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Simplify this solution 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!
