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

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

\[
g(x) = -2x + 3
\]

we need to set the equation equal to \(-3\) and solve for \(x\).

### Step-by-step solution:

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

\[
-2x + 3 = -3
\]

2. Subtract 3 from both sides:

\[
-2x = -3 - 3
\]

\[
-2x = -6
\]

3. Divide both sides by \(-2\):

\[
x = \frac{-6}{-2}
\]

\[
x = 3
\]

### Solution:

\[
x = 3
\]

Would you like more details or have any questions?

### Related Questions:

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

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

Learn how to solve the equation g(x) = -2x + 3 for x when g(x) equals -3. This problem involves linear equations and functions, with a detailed step-by-step solution provided.

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