Question

A construction crew is lengthening a road. The crew is adding 3 miles to the road each week. The road originally measured 62 miles long. The crew's goal is given by 3x + 62 > 110, where x is the number of weeks the crew works.
Complete the parts below.
(a) Solve the given inequality and graph the solution on the number line below
0-2-4-6-8-10-12-14-16-18-20-22-24-26-28-30

Answer 1

To solve the inequality \(3x + 62 > 110\), we will isolate \(x\).

1. Start by subtracting 62 from both sides:
\[
3x > 110 - 62
\]
\[
3x > 48
\]

2. Now, divide both sides by 3:
\[
x > \frac{48}{3}
\]
\[
x > 16
\]

So the solution to the inequality is \(x > 16\). This means that the crew needs to work more than 16 weeks to reach their goal.

### Graphing the solution on the number line:

On the number line provided (0 to 30), you would represent this solution by drawing an open circle over the point 16 (indicating that 16 is not included in the solution) and shading to the right (to indicate all values greater than 16).

```plaintext
0-2-4-6-8-10-12-14-16-18-20-22-24-26-28-30
o-------------------- (Shaded to the right)
```

This graph indicates that any value greater than 16 satisfies the inequality \(3x + 62 > 110\).