Math Problem Statement

Solve the set of linear equations provided in the image.

Solution

It looks like you've shared an image with a set of equations. Here’s a breakdown of the solutions based on the image you provided:

  1. Equation 9:
    6x8=7x166x - 8 = 7x - 16
    Solved: x=8x = 8.

  2. Equation 10:
    38x=6(6+6x)-38 - x = 6(6 + 6x)
    Solved: x=2x = 2.

  3. Equation 11:
    8(b5)=8b328(b - 5) = 8b - 32
    Solved: b=8b = 8.

  4. Equation 12:
    6m9=3(m+3)-6m - 9 = -3(m + 3)
    Solved: m=0m = 0.

  5. Equation 13:
    8(n+4)=32+8n8(n + 4) = 32 + 8n
    Solved: n=0n = 0.

  6. Equation 14:
    5(15x)=333x-5(1 - 5x) = -33 - 3x
    Solved: x=1.6x = -1.6.

  7. Equation 15:
    8k+4=4(52k)8k + 4 = 4(5 - 2k)
    Solved: k=1k = 1.

  8. Equation 16:
    4+5k7=31+5k4 + 5k - 7 = -31 + 5k
    Solved: k=0k = 0.

  9. Equation 17:
    7+8(x4)=378x-7 + 8(x - 4) = -37 - 8x
    Solved: x=2x = 2.

  10. Equation 18:
    (2+6p)=6p+3-(2 + 6p) = -6p + 3
    Solved: p=5p = 5.

Would you like a more detailed breakdown or further explanation for any of these problems? Feel free to ask!

Related Questions:

  1. How do you solve linear equations with variables on both sides?
  2. What are some techniques for simplifying complex equations before solving?
  3. How do you solve equations with fractions?
  4. What are some common mistakes when solving equations like these?
  5. How do you verify your solution to an equation?

Tip: Always check your solution by substituting it back into the original equation to verify it satisfies the equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Solving Equations with Variables on Both Sides
Simplifying Expressions

Formulas

Basic Linear Equation Form: ax + b = c
Distributive Property

Theorems

Solving Equations by Isolating the Variable

Suitable Grade Level

Grades 7-9