Math Problem Statement

  1. 2x + 11 2. (2z + y) - 5 3. |(y + z) - x| x is 20 y is 11 z is 21

Solution

Let's evaluate each expression using the given values: x=20x = 20, y=11y = 11, and z=21z = 21.

  1. For 2x+112x + 11: 2(20)+11=40+11=512(20) + 11 = 40 + 11 = 51

  2. For (2z+y)5(2z + y) - 5: (2(21)+11)5=(42+11)5=535=48(2(21) + 11) - 5 = (42 + 11) - 5 = 53 - 5 = 48

  3. For (y+z)x|(y + z) - x|: (11+21)20=3220=12=12|(11 + 21) - 20| = |32 - 20| = |12| = 12

Summary of Results:

  1. 2x+11=512x + 11 = 51
  2. (2z+y)5=48(2z + y) - 5 = 48
  3. (y+z)x=12|(y + z) - x| = 12

Do you want more details or have any questions about these calculations? Here are some related questions to consider:

  1. How would the results change if xx were increased by 5?
  2. What would be the results if zz were doubled?
  3. How do absolute values affect equations like the third one?
  4. Can you create similar expressions using different variables?
  5. What are other ways to manipulate these equations algebraically?

Tip: When substituting values into expressions, always double-check the order of operations to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Values
Basic Arithmetic Operations

Formulas

2x + 11
(2z + y) - 5
|(y + z) - x|

Theorems

Properties of absolute value

Suitable Grade Level

Grades 7-9