Question

use the drawing tools to form the correct answer on the number line. graph the solution to this inequality on the number line. 2x - 6 > -16 and 3x - 10 ≤ 8

Explanation:

Step1: Solve the first - inequality

Add 6 to both sides of $2x - 6>-16$: $2x-6 + 6>-16 + 6$, which simplifies to $2x>-10$. Then divide both sides by 2: $x > - 5$.

Step2: Solve the second - inequality

Add 10 to both sides of $3x-10\leq8$: $3x-10 + 10\leq8 + 10$, which simplifies to $3x\leq18$. Then divide both sides by 3: $x\leq6$.

Answer:

The solution of the compound - inequality is $-5 < x\leq6$. On the number line, there is an open circle at $x=-5$ (because $x > - 5$) and a closed circle at $x = 6$ (because $x\leq6$), and the line is shaded between these two points.