Which value is a solution to the inequality $2x - 5 < -12$?
A. 0
B. 3
C. -2
D. -4
Answer (1)
Substitute each given value into the inequality 2 x − 5 < − 12 .
For x = 0 , the inequality becomes − 5 < − 12 , which is false.
For x = 3 , the inequality becomes 1 < − 12 , which is false.
For x = − 2 , the inequality becomes − 9 < − 12 , which is false.
For x = − 4 , the inequality becomes − 13 < − 12 , which is true. Therefore, the solution is − 4 .
Explanation
Understanding the Problem We are given the inequality 2 x − 5 < − 12 and four possible solutions: 0, 3, -2, and -4. Our goal is to determine which of these values satisfies the inequality.
Solution Plan We will substitute each of the given values into the inequality and check if the inequality holds true. If it does, then the value is a solution.
Testing x = 0 Let's test x = 0 : 2 ( 0 ) − 5 < − 12 − 5 < − 12 This is false.
Testing x = 3 Now let's test x = 3 : 2 ( 3 ) − 5 < − 12 6 − 5 < − 12 1 < − 12 This is also false.
Testing x = -2 Next, we test x = − 2 : 2 ( − 2 ) − 5 < − 12 − 4 − 5 < − 12 − 9 < − 12 This is false as well.
Testing x = -4 Finally, we test x = − 4 : 2 ( − 4 ) − 5 < − 12 − 8 − 5 < − 12 − 13 < − 12 This is true.
Conclusion Therefore, the value x = − 4 is a solution to the inequality 2 x − 5 < − 12 .
Examples
Imagine you're trying to figure out how many hours you need to work to save a certain amount of money. If you need to save more than $100, and you earn $10 per hour but have to spend $20 on expenses, this problem is similar to figuring out how many hours you need to work to have more than $100 left after expenses. Inequalities help us determine the minimum number of hours needed to reach your savings goal.
