21.0k views
5 votes
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}

User Lmagyar
by
8.7k points

1 Answer

3 votes

Final answer:

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}.

User Omaha
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories