Which solution value satisfies the inequality [tex]x+10\ \textgreater \ 12[/tex]?
A) [tex]x=3[/tex]
B) [tex]x=2[/tex]
C) [tex]x=-1[/tex]
D) [tex]x=0[/tex]
Answer (1)
Substitute each given value into the inequality.
Check if the inequality holds true.
x = 3 gives 12"> 13 > 12 , which is true.
Therefore, the solution is 3 .
Explanation
Understanding the Problem We are given the inequality 12"> x + 10 > 12 and four possible solutions for x : 3, 2, -1, and 0. Our goal is to determine which of these values satisfies the inequality.
Solution Strategy We will substitute each given value of x into the inequality and check if the resulting statement is true.
Testing the Options Let's test each option:
A) x = 3 : Substituting x = 3 into the inequality gives 12"> 3 + 10 > 12 , which simplifies to 12"> 13 > 12 . This is true.
B) x = 2 : Substituting x = 2 into the inequality gives 12"> 2 + 10 > 12 , which simplifies to 12"> 12 > 12 . This is false.
C) x = − 1 : Substituting x = − 1 into the inequality gives 12"> − 1 + 10 > 12 , which simplifies to 12"> 9 > 12 . This is false.
D) x = 0 : Substituting x = 0 into the inequality gives 12"> 0 + 10 > 12 , which simplifies to 12"> 10 > 12 . This is false.
Conclusion Only x = 3 satisfies the inequality 12"> x + 10 > 12 . Therefore, the solution is x = 3 .
Examples
Imagine you're saving money and need to have more than $12 in your account. If you currently have $10, this problem helps you determine how much more money you need to deposit to reach your goal. By understanding inequalities, you can easily calculate the minimum amount required to exceed a certain threshold, whether it's savings, expenses, or any other real-life scenario where you need to surpass a specific value.
