Ask a New Question
Menu

Look at the inequality below.

-2x+4≥0

Which of the following represents the solution to the inequality?

3 answers

To solve the inequality \(-2x + 4 \geq 0\), follow these steps:

  1. Subtract 4 from both sides: \[ -2x \geq -4 \]

  2. Divide both sides by -2 (remember to reverse the inequality sign when dividing by a negative number): \[ x \leq 2 \]

So, the solution to the inequality \(-2x + 4 \geq 0\) is \(x \leq 2\).

This means that the values of \(x\) that satisfy the inequality are all real numbers less than or equal to 2.

number line

To represent the solution \( x \leq 2 \) on a number line, you can follow these steps:

  1. Draw a horizontal line: This represents your number line.

  2. Mark and label some key points: Include the point \(2\) and a few points before and after it (for example, \(0\), \(1\), \(2\), \(3\), and \(4\)).

  3. Draw a closed circle at the point \(2\): The closed circle indicates that \(2\) is included in the solution set (since the inequality is "less than or equal to").

  4. Shade to the left of \(2\): This shading represents all the numbers that are less than \(2\).

Here’s how it should look visually:

---|---|---|---|---|---|---|---|---|---
   0   1   2   3   4

      <------●

The closed circle at \(2\) indicates that \(2\) is part of the solution, and the arrow pointing to the left represents all numbers less than \(2\).