Question

use the drawing tools to form the correct answer on the number line.
graph the solution set to this inequality
-2x + 9 ≤ 5x - 12
drawing tools
select
point
open point
ray
click on a tool to begin drawing undo reset
-10 -8 -6 -4 -2 0 2 4 6 8 10

Explanation:

Step1: Add \(2x\) to both sides

To isolate the \(x\) terms, we add \(2x\) to both sides of the inequality \(-2x + 9\leq5x - 12\). This gives us \(9\leq7x - 12\).

Step2: Add 12 to both sides

Next, we add 12 to both sides to isolate the term with \(x\). So, \(9 + 12\leq7x\), which simplifies to \(21\leq7x\).

Step3: Divide by 7

Now, we divide both sides by 7 to solve for \(x\). \(\frac{21}{7}\leq x\), so \(x\geq3\).

To graph this on the number line:

• First, use the "Point" tool to mark a closed point at \(x = 3\) (since the inequality is \(\leq\), we use a closed point).
• Then, use the "Ray" tool to draw a ray starting at \(x = 3\) and pointing to the right (since \(x\) is greater than or equal to 3, the solution set includes all numbers to the right of 3).

Answer:

The solution to the inequality is \(x\geq3\). On the number line, mark a closed point at 3 and draw a ray to the right from 3.