Math Problem Statement

Given g, of, x, equals, minus, 5, x, plus, 5g(x)=−5x+5, solve for xx when g, of, x, equals, 0g(x)=0.

Solution

To solve for xx when g(x)=0g(x) = 0 in the function g(x)=5x+5g(x) = -5x + 5, follow these steps:

  1. Set g(x)g(x) to 0, as given: 0=5x+50 = -5x + 5

  2. Solve for xx by isolating it on one side: 5x=5-5x = -5

  3. Divide both sides by -5: x=1x = 1

Thus, the solution is: x=1x = 1

Would you like further details on this solution, or do you have additional questions?

Here are some related questions for further practice:

  1. What would be the value of g(x)g(x) if x=2x = 2?
  2. If g(x)=5x+cg(x) = -5x + c, how does the value of xx change when g(x)=0g(x) = 0 with different values of cc?
  3. How would the solution change if the equation were g(x)=3x+5g(x) = -3x + 5?
  4. What is the slope of the function g(x)=5x+5g(x) = -5x + 5, and how does it affect the solution?
  5. How does shifting the function g(x)=5x+5g(x) = -5x + 5 vertically impact the point where g(x)=0g(x) = 0?

Tip: When solving linear equations, isolate the variable by performing inverse operations in the correct sequence (addition/subtraction, then multiplication/division).

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Standard form of a linear equation: ax + b = 0

Theorems

Basic principles of solving linear equations

Suitable Grade Level

Grades 6-8