Solving g(x)=-x+4 > 0: Linear Function Inequality Analysis

Question

Look at the graph below of the following functions:

$f(x)=x^2-6x+8$

$g(x)=-x+4$

For which values of x is
$g(x)>0$ true?

To solve the problem of finding for which values of $x$ , the function $g(x) = -x + 4$ is greater than zero, we begin as follows:

Step 1: Set up the inequality $g(x) > 0$ . This translates to $-x + 4 > 0$ .
Step 2: Solve the inequality:
- Subtract 4 from both sides: $-x > -4$ .
- Multiply both sides by $-1$ , reversing the inequality: $x < 4$ .

Therefore, the solution to the problem is that $g(x) > 0$ when $x < 4$ .

The corresponding choice that reflects this solution is choice 4: $x < 4$ .

$x<4$