Math Problem Statement

Solve for x in a series of linear equations and geometric angle relationships, including problems involving adjacent, vertical, complementary, and supplementary angles.

Solution

Let's go over the problems you've worked on based on the image.

  1. Problem 13 (Solving for x):

    • Equations: 9x+0+5x11=7x99x + 0^\circ + 5x - 11^\circ = 7x - 9^\circ
    • Your steps show combining like terms on the left-hand side: 14x11=7x914x - 11^\circ = 7x - 9^\circ.
    • By adding 7x7x to both sides and solving for xx, you found x=2x = -2.

    That looks correct!

  2. Problem 14 (Solving for mGEFm\angle GEF):

    • Equation: mGEF=5(mDEG)13m\angle GEF = 5(m\angle DEG) - 13 with mDEF=149m\angle DEF = 149^\circ.
    • Your approach is unclear from the image, but you'll need to substitute the given values and solve accordingly.
  3. Problem 15 (Solving for x):

    • Equation: 7x1=6x17x - 1 = 6x - 1.
    • You simplified this to x=1x = 1, which is correct!
  4. Problem 16 (Solving for x):

    • Equation: 5x+4=8x715x + 4^\circ = 8x - 71^\circ.
    • You simplified to x=25x = 25, which is correct!
  5. Problem 17 (Finding missing values):

    • The given angles involve perpendicular lines (indicating 90° relationships).
    • Your setup looks correct, but there is more space to solve for the missing values.

Would you like detailed steps for any of these problems? Here are some questions for further practice:

  1. Can you confirm how to calculate mGEFm\angle GEF from problem 14?
  2. How would you approach solving for the missing values in problem 17?
  3. Why is x=1x = 1 correct in problem 15?
  4. How do perpendicular lines help with finding missing angles in problem 17?
  5. What are other methods to check solutions for linear equations?

Tip: Always double-check your final equations for any arithmetic mistakes.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Geometric Angle Relationships

Formulas

Linear equation: ax + b = cx + d
Angle sum: Supplementary angles sum to 180°
Vertical angles are equal
Adjacent angles form a linear pair

Theorems

Supplementary Angle Theorem
Vertical Angles Theorem

Suitable Grade Level

Grades 8-10