Question

a construction crew is lengthening a road. the crew is adding 6 miles to the road each week. the road originally measured 58 miles long. the crews goal is given by $6x + 58>142$, 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.

Explanation:

Step1: Subtract 58 from both sides

$$6x+58 - 58>142 - 58$$
$$6x>84$$

Step2: Divide both sides by 6

$$\frac{6x}{6}>\frac{84}{6}$$
$$x > 14$$

To graph \(x>14\) on the number - line:

• Place an open circle at \(x = 14\) (because \(x\) is not equal to 14, only greater than 14).
• Draw an arrow to the right of 14 to represent all the values of \(x\) that satisfy the inequality.

Answer:

The solution of the inequality \(6x + 58>142\) is \(x>14\). On the number - line, there is an open circle at 14 and an arrow pointing to the right.