Question

seventh grade 〉 u.8 graph solutions to two - step inequalities 6tt
solve the inequality and graph the solution.
17 - 8z > 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.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 17 from both sides

To isolate the term with \( z \), we subtract 17 from both sides of the inequality \( 17 - 8z > 1 \). This gives us \( 17 - 17 - 8z > 1 - 17 \), which simplifies to \( -8z > -16 \).

Step2: Divide by -8 (reverse inequality)

When dividing both sides of an inequality by a negative number, we must reverse the inequality sign. So, dividing both sides of \( -8z > -16 \) by -8 gives \( z < \frac{-16}{-8} \), which simplifies to \( z < 2 \).

Step3: Graph the solution

On the number line, we plot an open circle at 2 (since the inequality is \( z < 2 \), not \( z \leq 2 \)) and draw an arrow to the left to represent all numbers less than 2.

Answer:

The solution to the inequality \( 17 - 8z > 1 \) is \( z < 2 \). To graph it, place an open circle at 2 on the number line and draw an arrow pointing to the left.