Question

solve the inequality and graph the solution.
2(f + 8) - 5 > 7
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

$2(f + 8)-5=2f+16 - 5=2f + 11$. So the inequality becomes $2f+11>7$.

Step2: Subtract 11 from both sides

$2f+11 - 11>7 - 11$, which simplifies to $2f>-4$.

Step3: Divide both sides by 2

$\frac{2f}{2}>\frac{-4}{2}$, resulting in $f>-2$.

To graph the solution:

• The endpoint is $f = - 2$. Since the inequality is $f>-2$, we use an open - circle at $f=-2$ on the number line.
• Then we draw a ray to the right of $f = - 2$ to represent all the values of $f$ that satisfy the inequality.

Answer:

The solution of the inequality is $f>-2$. On the number line, there is an open - circle at $-2$ and a ray extending to the right.