Question

-2x+4 if x<5 f(x) = -5x+2 if x > 5 The second one is greater than it equal to____

Answer 1

The expression -5x+2 is greater than or equal to -2x+4 when
`\(x \leq -2\)`.

Step-by-step explanation:

To determine when -5x+2 is greater than or equal to -2x+4, we can set up the inequality and solve for x:

`\[ -5x + 2 \geq -2x + 4 \]`

First, we can simplify the inequality by subtracting -2x from both sides:

`\[ -3x + 2 \geq 4 \]`

Next, subtract 2 from both sides to isolate the term with x:

`\[ -3x \geq 2 \]`

Now, divide both sides by -3, remembering to reverse the inequality sign when dividing by a negative number:

`\[ x \leq -(2)/(3) \]`

So, the expression -5x+2 is greater than or equal to -2x+4
`\(x \leq -(2)/(3)\).` Therefore, the solution is
`\(x \leq -(2)/(3)\)`.

Understanding how to solve and interpret inequalities is fundamental in analyzing the relationship between two expressions. In this case, recognizing the solution
`\(x \leq -(2)/(3)\)` provides the range of values for which -5x+2 is greater than or equal to -2x+4.