Solve the compound inequality. Write the solution in interval notation.
-0.4

Question

Solve the compound inequality. Write the solution in interval notation.
-0.4 < 0.4x - 0.7 < 1.3
A)[2.75, 5]
B)(0, 5)
C)(-0.75, 1.5)
D)(2.75, 5)

Quizplus · Accepted Answer

First, we add 0.7 to all three parts of the inequality to get:
1.1 < 0.4x < 2
Then, we divide all parts by 0.4 (and we switch the direction of the inequality signs since we are dividing by a negative number) to get:
2.75 < x < 5
Finally, we write this solution in interval notation: (2.75, 5). Therefore, the answer is D. To solve this compound inequality, we need to isolate x in the middle of the inequality. 
Adding 0.7 to all parts of the inequality, we get:
1.1 < 0.4x < 2.0
Dividing all parts of the inequality by 0.4 (since we want to isolate x), we get:
2.75 < x < 5
Therefore, the solution is the interval (2.75, 5). 
Choice D represents this interval and is therefore the best choice.

Solve the Compound Inequality