Math Problem Statement

Given g, of, x, equals, minus, 2, x, plus, 3g(x)=−2x+3, solve for xx when g, of, x, equals, minus, 3g(x)=−3

Solution

To solve for xx when g(x)=3g(x) = -3 and the function is given by:

g(x)=2x+3g(x) = -2x + 3

we need to set the equation equal to 3-3 and solve for xx.

Step-by-step solution:

  1. Set g(x)=3g(x) = -3:

2x+3=3-2x + 3 = -3

  1. Subtract 3 from both sides:

2x=33-2x = -3 - 3

2x=6-2x = -6

  1. Divide both sides by 2-2:

x=62x = \frac{-6}{-2}

x=3x = 3

Solution:

x=3x = 3

Would you like more details or have any questions?

Related Questions:

  1. What is the value of xx when g(x)=0g(x) = 0?
  2. How do you find the inverse of g(x)=2x+3g(x) = -2x + 3?
  3. What is the slope of the line represented by g(x)=2x+3g(x) = -2x + 3?
  4. If g(x)=2x+3g(x) = -2x + 3, what is g(2)g(2)?
  5. What is the y-intercept of the function g(x)=2x+3g(x) = -2x + 3?

Tip: When solving equations, always perform the same operation on both sides to maintain the equation's balance.

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Math Problem Analysis

Mathematical Concepts

Linear equations
Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9