Question

solve the inequality and graph the solution.
w - 8 ≥ 1
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
number line from 0 to 10 with ticks at 0,1,2,3,4,5,6,7,8,9,10

Explanation:

Step1: Add 8 to both sides

To solve the inequality \( w - 8 \geq 1 \), we add 8 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the inequality remains true. So, we have:

\( w - 8 + 8 \geq 1 + 8 \)

Step2: Simplify both sides

Simplifying the left - hand side, \( w-8 + 8=w \). Simplifying the right - hand side, \( 1 + 8 = 9 \). So the solution to the inequality is \( w\geq9 \).

For graphing the solution:

• We plot a closed dot (since the inequality is "greater than or equal to") at \( w = 9 \) on the number line.
• Then we draw an arrow starting from the closed dot at 9 and pointing to the right (because we want all values of \( w \) that are greater than or equal to 9).

Answer:

The solution to the inequality \( w - 8\geq1 \) is \( w\geq9 \). To graph it, plot a closed dot at 9 on the number line and draw an arrow to the right.