Math Problem Statement

Solve the equations provided in the 'You Try It' section of the worksheet, showing all work for each step.

Solution

Here are the solutions for the "You Try It" section of the worksheet. I will show all work for each step as requested:

  1. Solve x7=3\frac{x}{7} = 3:

    Multiply both sides of the equation by 7 to isolate xx: x=37x = 3 \cdot 7 x=21x = 21

  2. Solve m2=8\frac{-m}{2} = -8:

    Multiply both sides of the equation by 2 to eliminate the denominator: m=82-m = -8 \cdot 2 m=16-m = -16 Divide both sides by 1-1 to solve for mm: m=16m = 16

  3. Solve 6=w46 = \frac{-w}{4}:

    Multiply both sides of the equation by 4 to eliminate the denominator: 64=w6 \cdot 4 = -w 24=w24 = -w Divide both sides by 1-1 to solve for ww: w=24w = -24

Let me know if you need further explanations or clarifications.

Questions to Expand Learning:

  1. Why does multiplying by the denominator work to solve these types of equations?
  2. How does changing the sign of a variable impact the solution of the equation?
  3. Could you solve these equations if the fractions included decimals instead? How?
  4. What happens if both the numerator and denominator are negative in a fraction?
  5. How can these methods be extended to solve more complex equations with multiple fractions?

Tip:

When solving equations with fractions, always check your solution by substituting it back into the original equation to ensure it balances!

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Math Problem Analysis

Mathematical Concepts

Solving equations
Fractions
Negative numbers

Formulas

Fraction elimination by multiplication
Sign adjustment for variables

Theorems

Equality property of multiplication
Sign property of fractions

Suitable Grade Level

Grades 6-8