swerve wrote:
The number line above represents which of the following inequalities?
A. \(x < 1\)
B. \(-6 < 2x < 2\)
C. \(-9 < 3x < 6\)
D. \(1 < 2x < 3\)
E. \(x > -3\)
The OA is
B
Source: Manhattan Prep
We can also solve the question by
testing the answer choices
Here's what I mean:
The diagram tells us that
x= 0 is a solution to the inequality.
When we check the answer choices, we see that answer choice D (1 < 2x < 3) does NOT have x = 0 as a solution.
When we let x = 0, the inequality becomes 1 < 2(0) < 3. In other words, 1 < 0 < 3
No good! ELIMINATE D
The diagram also tells us that
x= 1.5 is NOT a solution to the inequality.
When we check the answer choices, we see that answer choices C and E say that x = 1.5 IS a solution.
C. -9 < 3x < 6. Replace x with 1.5 to get: -9 < 4.5 < 6. Works! Since answer C says that x COULD equal 1.5, we can eliminate answer choice C
E. x > -3. Replace x with 1.5 to get: 1.5 > -3. Works! Since answer E says that x COULD equal 1.5, we can eliminate answer choice E.
We're down to answer choices A and B
The diagram tells us that
x= -5 is NOT a solution to the inequality.
When we check the answer choices, we see that answer choice A say that x = -5 IS a solution.
A. x < 1. Replace x with -5 to get: -5 < 1. Works! Since answer A says that x COULD equal -5, we can eliminate answer choice A
By the process of elimination, we're left with...
Answer: B
Cheers,
Brent
