Question

If 8x + 5 > 1, 2x - 7 < 3, and x is an integer, which of the following is the set of all possible values of x?

a) {1, 2, 3, 4}
b) {0, 1, 2, 3, 4}
c) {-1, 0, 1, 2, 3, 4}
d) {-1, 0, 1, 2, 3, 4, 5}

Answer 1

Given two inequalities 8x + 5 > 1 and 2x - 7 < 3, the set of all possible integer values for x is {0, 1, 2, 3, 4}, which corresponds to option b).

Step-by-step explanation:

The student has asked for the set of all possible integer values of x given two inequalities, 8x + 5 > 1, and 2x - 7 < 3. To solve this, we need to isolate x in each inequality and then see the intersection of the two solution sets.

First inequality:

8x + 5 > 1

8x > 1 - 5

8x > -4

x > -0.5

Since x is an integer, x must be equal to or greater than 0.

Second inequality:

2x - 7 < 3

2x < 3 + 7

2x < 10

x < 5

Given that x is an integer, x can be 0, 1, 2, 3, or 4.

By combining both inequalities, we find that x can be 0, 1, 2, 3, or 4. Therefore, the correct answer is option b) {0, 1, 2, 3, 4}.