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A construction crew is lengthening a road. The crew is adding 6 miles to the road each week. The road...

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 crew's 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.
(b) Choose and complete the statement that best describes the solution.
- The crew's goal is to lengthen the road to less than ⬜ miles. This will take more than ⬜ weeks.
- The crew's goal is to lengthen the road to more than ⬜ miles. This will take less than ⬜ weeks.
- The crew's goal is to lengthen the road to more than ⬜ miles. This will take more than ⬜ weeks.

Answer

(a) Solve the inequality: 6x + 58 > 142

  1. Subtract 58 from both sides: 6x > 84
  2. Divide both sides by 6: x > 14

Graph the solution on the number line: Shade the region to the right of 14, indicating x > 14.

(b) The crew's goal is to lengthen the road to more than 142 miles. This will take more than 14 weeks.

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