It is given that PQ=RS, and the diagram shows that PQ=x−1 and RS=3x−7. Therefore, the equation x−1=3x−7 must be true. Solving this equation for x leads to 0 2x = 6, so x = 3. The length of segment PS is the sum of the lengths of PQ, QR, and RS, which is (x−1)+x+(3x−7), or equivalently 5x−8. Substituting 3 for x in this expression gives 5(3)−8=7.