Asked by Shane Cornfield on May 21, 2024
Verified
Solve the inequality x−1x−5≤3\frac { x - 1 } { x - 5 } \leq 3x−5x−1≤3 and graph the solution on the real number line.
A) Solution: (5,∞) ( 5 , \infty ) (5,∞)
B) Solution: (0,∞) ( 0 , \infty ) (0,∞)
C) Solution: (−∞,0) ∪[7,∞) ( - \infty , 0 ) \cup [ 7 , \infty ) (−∞,0) ∪[7,∞)
D) Solution: (−∞,5) ∪[7,∞) ( - \infty , 5 ) \cup [ 7 , \infty ) (−∞,5) ∪[7,∞)
E) Solution: (−∞,∞) ( - \infty , \infty ) (−∞,∞)
Real Number Line
A one-dimensional line on which every point corresponds to a real number and every real number to a point.
- Represent the solutions to inequalities on a real numerical line.
Verified Answer
AS
Alicia SerranoMay 23, 2024
Final Answer :
D
Explanation :
Multiplying both sides by the denominator, we get $x-1\leq 3(x-5)$, which simplifies to $x\geq 7$ or $x\leq 5$. The solution is the union of these two intervals, which is $(-\infty, 5]\cup[7,\infty)$. Therefore, the correct choice is (D).
Learning Objectives
- Represent the solutions to inequalities on a real numerical line.
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