Check: LHS = |16 - 5| = 11, RHS = |8 + 3| = 11 → valid. - Abu Waleed Tea
Understanding Absolute Value Equality: Checking |16 - 5| = |8 + 3| = 11
Understanding Absolute Value Equality: Checking |16 - 5| = |8 + 3| = 11
When working with absolute values in mathematics, one essential skill is verifying whether two expressions inside the absolute value symbols are truly equal. In this article, we explore and validate the equation:
LHS = |16 - 5| = 11
RHS = |8 + 3| = 11
Is this statement valid? Let’s break it down step by step.
Understanding the Context
What is Absolute Value?
The absolute value of a number represents its distance from zero on the number line, regardless of direction. This means:
- |a| = a if a ≥ 0
- |a| = -a if a < 0
Key Insights
In both cases, the result is always non-negative.
Step 1: Simplify the Left-Hand Side (LHS)
LHS = |16 - 5|
First, compute the difference inside the absolute value:
16 - 5 = 11
Now apply absolute value:
|11| = 11
So, LHS = 11
🔗 Related Articles You Might Like:
📰 Thus, the largest multiple of 6 less than 20 is 18, and it satisfies \( 18^3 = 5832 < 8000 \). Therefore, the largest possible value of \( p \) is \(\boxed{18}\). 📰 Question:** A virologist is studying viral loads and notes that a particular parameter \( v \) is a positive integer less than or equal to 30. If the probability that \( v \) is a factor of 360 is to be calculated, what is this probability? 📰 First, we determine the number of positive integers \( v \) that are factors of 360 and are less than or equal to 30. Begin by finding the prime factorization of 360:Final Thoughts
Step 2: Simplify the Right-Hand Side (RHS)
RHS = |8 + 3|
First, compute the sum inside the absolute value:
8 + 3 = 11
Now apply absolute value:
|11| = 11
So, RHS = 11
Step 3: Compare Both Sides
We have:
LHS = 11 and RHS = 11
Since both sides are equal, the equation |16 - 5| = |8 + 3| holds true.
Why This Matters: Checking Validity with Absolute Values
Absolute value expressions often appear in geometry, algebra, and equations involving distances. Validating such expressions ensures accuracy in problem-solving and protects against errors in calculations. The key takeaway is:
If |A| = |B|, then A = B or A = -B. But in this case, LHS = RHS = 11, confirming equality directly.
