Math Problem Statement

  1. 2x + 11 2. (2z + y ) - 5 3. |(y + z) - x| x is 0 y is 21 z is 20

Solution

Let's evaluate each expression given the values:

  1. Expression: 2x+112x + 11

    • Substitute x=0x = 0: 20+11=0+11=112 \cdot 0 + 11 = 0 + 11 = 11
  2. Expression: (2z+y)5(2z + y) - 5

    • Substitute z=20z = 20 and y=21y = 21: (220+21)5=(40+21)5=615=56(2 \cdot 20 + 21) - 5 = (40 + 21) - 5 = 61 - 5 = 56
  3. Expression: (y+z)x|(y + z) - x|

    • Substitute x=0x = 0, y=21y = 21, and z=20z = 20: (21+20)0=410=41=41|(21 + 20) - 0| = |41 - 0| = |41| = 41

Final Answers:

  1. 2x+11=112x + 11 = 11
  2. (2z+y)5=56(2z + y) - 5 = 56
  3. (y+z)x=41|(y + z) - x| = 41

Would you like further details or have any other questions?

Related Questions:

  1. How would the results change if xx, yy, or zz were negative?
  2. What if xx were a non-zero value? How would that affect the first expression?
  3. Can you find the result for x(y+z)|x - (y + z)| with the same values?
  4. What if we add another operation to these expressions? How would the results vary?
  5. Can you explore similar expressions with powers, such as 2x2+112x^2 + 11?

Tip: Absolute values make negative results positive, so they’re often used to measure "distance" between values, keeping outcomes non-negative.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value
Substitution

Formulas

Linear expression: ax + b
Expression involving variables: (2z + y) - c
Absolute value expression: |(y + z) - x|

Theorems

Absolute value properties

Suitable Grade Level

Grades 6-8