Question

If -4<3x-1<5 , then the values of x that satisfy the compound inequality are

(A) -2
(B) -1
(C) -1
(D) 0
(E) 1

Answer 1

The values of x that satisfy the inequality -4 < 3x - 1 < 5 are x greater than -1 and less than 2, therefore, the correct values from the given options are -1, 0, and 1.

Step-by-step explanation:

The question asks to find the values of x that satisfy the compound inequality -4 < 3x - 1 < 5. To solve for x, we need to perform two separate inequality operations. First, we add 1 to all parts of the inequality to get -3 < 3x < 6. Next, we divide every part by 3 to isolate x, resulting in -1 < x < 2.

From the given options, (-2) is less than -1, (-1) is equal to -1, (0) and (1) fall within the range, and (E) 1 is valid, but we need to identify all values within the inequality range, so the correct answers are (B) -1, (D) 0, and (E) 1.