SAT Mathematics Practice Test 5

It is given that $\mathit{P}\mathit{Q}=\mathit{R}\mathit{S},$ and the diagram shows that $\mathit{P}\mathit{Q}=\mathit{x}-1$ and $\mathit{R}\mathit{S}=3\mathit{x}-7$. Therefore, the equation $\mathit{x}-1=3\mathit{x}-7$ must be true. Solving this equation for $\mathit{x}$ 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 $\left(\mathit{x}-1\right)+\mathit{x}+\left(3\mathit{x}-7\right),$ or equivalently $5\mathit{x}-8.$ Substituting $3$ for x in this expression gives $5\left(3\right)-8=7.$