Math Problem Statement

Use k = 5 and d = 6 to solve k - 4d, use k = -4 and z = 5 to solve -5(3z - 2k), and use s = 8 and w = -4 to solve -6 + 5/4 - 8w.

Solution

The image you provided contains several algebraic expressions that require substitution of given values. Let's go through each of them step by step:

Problem 2) k4dk - 4d

  • Given: k=5k = 5 and d=6d = 6
  • Substitution: 54(6)5 - 4(6)
  • Calculation: 524=195 - 24 = -19
  • Final Answer: 19-19

Problem 3) 5(3z2k)-5(3z - 2k)

  • Given: k=4k = -4 and z=5z = 5
  • Substitution: 5(3(5)2(4))-5(3(5) - 2(-4))
  • Calculation: 5(15+8)=5(23)=115-5(15 + 8) = -5(23) = -115
  • Final Answer: 115-115

Problem 4) 6+548w-6 + \frac{5}{4} - 8w

  • Given: s=8s = 8 and w=4w = -4
  • Substitution: 6+548(4)-6 + \frac{5}{4} - 8(-4)
  • Calculation: 6+54+32-6 + \frac{5}{4} + 32 6+32+54=26+54=26+1.25=27.25-6 + 32 + \frac{5}{4} = 26 + \frac{5}{4} = 26 + 1.25 = 27.25
  • Final Answer: 27.2527.25

Would you like any further details on these solutions, or do you have any other questions?


Here are five related questions to practice:

  1. What is the result of substituting k=7k = 7 and d=2d = 2 into the expression k4dk - 4d?
  2. If z=3z = 3 and k=2k = 2, what is the value of 5(3z2k)-5(3z - 2k)?
  3. Solve 6+327w-6 + \frac{3}{2} - 7w when w=5w = 5.
  4. What happens to the expression k4dk - 4d if dd is doubled?
  5. How would the answer to 5(3z2k)-5(3z - 2k) change if both zz and kk are negative?

Tip: When dealing with algebraic expressions, always remember to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution
Simplification

Formulas

Substitution into algebraic expressions
Order of operations (PEMDAS)

Theorems

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Suitable Grade Level

Grades 6-8