Math Problem Statement

2∣−14−(−4)∣−18

Solution

Let's break down the expression step by step:

We are given:

214(4)182 \cdot \left| -14 - (-4) \right| - 18

Step 1: Simplify the inside of the absolute value.

14(4)=14+4=10-14 - (-4) = -14 + 4 = -10

So the expression becomes:

210182 \cdot \left| -10 \right| - 18

Step 2: Evaluate the absolute value.

The absolute value of 10-10 is 10, since absolute value represents the distance from zero on the number line.

210182 \cdot 10 - 18

Step 3: Multiply and simplify.

210=202 \cdot 10 = 20

So the expression becomes:

2018=220 - 18 = 2

Final Answer:

2\boxed{2}


Do you need any further clarification on this, or would you like to explore more related topics?

Here are some additional questions you can try:

  1. How would the expression change if the absolute value was on a different part of the expression, such as 14(4)| -14 | - (-4)?
  2. What happens if we replace 14-14 with 12-12 in the original expression?
  3. How do you handle absolute value expressions when they are combined with addition or subtraction?
  4. Can absolute value expressions ever result in a negative number?
  5. What are the properties of absolute value functions and their graphs?

Tip: Remember that absolute value always results in a non-negative number, regardless of whether the number inside is positive or negative.

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Order of Operations
Arithmetic Operations

Formulas

|a| = a if a ≥ 0, |a| = -a if a < 0

Theorems

Absolute Value Properties

Suitable Grade Level

Grades 6-8