Math Problem Statement

Solve the literal equation for y: 2x - 4y = 20.

Solution

To solve the given literal equation for yy:

2x4y=202x - 4y = 20

Follow these steps:

  1. Isolate the term involving yy: 4y=202x-4y = 20 - 2x This was achieved by subtracting 2x2x from both sides of the equation.

  2. Solve for yy: y=202x4y = \frac{20 - 2x}{-4}

  3. Simplify the expression: Break the fraction into two terms: y=2042x4y = \frac{20}{-4} - \frac{2x}{-4} Simplifying each term: y=5+x2y = -5 + \frac{x}{2}

Thus, the solution is: y=x25y = \frac{x}{2} - 5

Would you like more details on any step? Here are some related questions for practice:

  1. What would the equation look like if solved for xx instead of yy?
  2. How would the graph of the equation y=x25y = \frac{x}{2} - 5 look?
  3. What is the slope and y-intercept of the line given by the equation y=x25y = \frac{x}{2} - 5?
  4. How would you solve this equation if it involved a more complicated fraction?
  5. What happens if the right-hand side of the original equation changes to a different constant, such as 30?

Tip: Always try to simplify fractions early to make your calculations easier!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

y = (x/2) - 5

Theorems

Properties of Linear Equations

Suitable Grade Level

Grades 8-10