solve if x=11. x+44/2x
The correct answer and explanation is:
Let’s solve the expression step by step:
Given:
x+442xx + \frac{44}{2x}
with x=11x = 11.
Step 1: Substitute the value of xx
11+442×1111 + \frac{44}{2 \times 11}
Step 2: Simplify the denominator in the fraction
11+442211 + \frac{44}{22}
Step 3: Divide numerator by denominator
11+211 + 2
Step 4: Add the two numbers
1313
Final answer:
13\boxed{13}
Explanation:
This expression combines a simple addition and a division involving a variable xx. The key to solving it correctly is to substitute the value of xx first, then simplify the fraction carefully.
The expression is: x+442xx + \frac{44}{2x}
First, we substitute x=11x = 11: 11+442×1111 + \frac{44}{2 \times 11}
Calculate the denominator in the fraction: 2×11=222 \times 11 = 22
Now the expression is: 11+442211 + \frac{44}{22}
Next, simplify the fraction: 4422=2\frac{44}{22} = 2
Then add this result to 11: 11+2=1311 + 2 = 13
This step-by-step process highlights the importance of following the order of operations (PEMDAS/BODMAS): parentheses first (substitution), then multiplication in the denominator, division, and finally addition. Ignoring the order can lead to errors such as dividing incorrectly or mixing up terms.
In practical terms, this expression represents a combination of a linear term xx and a rational term 442x\frac{44}{2x}. For x=11x = 11, the rational term simplifies nicely because 44 divided by 22 gives a whole number (2), making the total sum easy to calculate.
This problem is a straightforward example of algebraic substitution and simplification that strengthens understanding of fractions and order of operations.