Solve the inequality. Write the solution set in interval notation.
-$$\frac { 7 } { 1 - x } \leq \frac { 2 } { 3 - x }$$
A) $\left( - \infty , \frac { 19 } { 5 } \right]$
B) $( 1,3 )$
C) $( - \infty , 1 ) \cup ( 3 , \infty )$
D) $( 1,3 ) \cup \left[ \frac { 19 } { 5 } , \infty \right]$

Question

Quizplus · Accepted Answer

To solve the inequality, cross-multiply to get $7(3-x) \leq 2(1-x)$. Simplifying gives $21 - 7x \leq 2 - 2x$. Rearranging terms, we get $5x \leq 19$, so $x \leq \frac{19}{5}$. The critical points are $x = 1$ and $x = 3$ where the original fractions are undefined. Testing intervals, the solution is $(1, 3) \cup \left[\frac{19}{5}, \infty\right)$.

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