Evaluate  |x3-(3-y)z|x| |                   if   x=-2, y=-12 and z=2.    



We are given the expression:

\[
|x^3 - (3 - y)z|x|
\]

and the values \( x = -2 \), \( y = -12 \), and \( z = 2 \). Let's evaluate this step by step.

### Step 1: Calculate \( x^3 \)
\[
x^3 = (-2)^3 = -8
\]

### Step 2: Simplify the term \( (3 - y)z \)
First, calculate \( 3 - y \):
\[
3 - (-12) = 3 + 12 = 15
\]
Now multiply by \( z \):
\[
(3 - y)z = 15 \times 2 = 30
\]

### Step 3: Substitute values into the expression
Now substitute these values into the expression:
\[
|x^3 - (3 - y)z|x| = |-8 - 30| \times |x|
\]

### Step 4: Simplify the expression inside the absolute value
\[
-8 - 30 = -38
\]
Thus:
\[
|x^3 - (3 - y)z| = |-38| = 38
\]

### Step 5: Calculate \( |x| \)
Since \( x = -2 \):
\[
|x| = |-2| = 2
\]

### Step 6: Final computation
Now, multiply the results:
\[
38 \times 2 = 76
\]

### Final Answer:
\[
\boxed{76}
\]

Let me know if you'd like a more detailed explanation of any step!

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Here are 5 related questions for further practice:
1. Evaluate \( |x^3 - (3 - y)z|x| \) if \( x = 1 \), \( y = 5 \), and \( z = 3 \).
2. What is the result of \( |x^2 - (4 - y)z| \) when \( x = -1 \), \( y = 7 \), and \( z = 2 \)?
3. Find the value of \( x^2 + (2 + y)z \) for \( x = 3 \), \( y = -4 \), and \( z = 1 \).
4. Simplify \( (x^3 + yz) |x| \) when \( x = -3 \), \( y = 2 \), and \( z = 4 \).
5. Calculate \( |x + y|z \) when \( x = -5 \), \( y = 2 \), and \( z = -3 \).

**Tip**: When working with absolute values, always simplify the expression inside first before taking the absolute value!

Evaluate |x^3 - (3 - y)z|x| if x=-2, y=-12 and z=2.

Learn how to evaluate the expression |x^3 - (3 - y)z|x| step by step with the values x=-2, y=-12, and z=2. This algebraic problem covers concepts of exponents, absolute value, and substitution, making it suitable for students in Grades 8-10.

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