Which solution value satisfies the inequality [tex]x-6 \geq -7[/tex]?
A) [tex]x=0[/tex]
B) [tex]x=-2[/tex]
C) [tex]x=-7[/tex]
D) [tex]x=-5[/tex]
Answer (1)
Substitute each given value into the inequality.
Check if the inequality holds true.
x = 0 gives − 6 ≥ − 7 , which is true.
The solution is 0 .
Explanation
Understanding the problem We are given the inequality x − 6 ≥ − 7 and four possible solutions: A) x = 0 , B) x = − 2 , C) x = − 7 , D) x = − 5 . Our goal is to find which value of x satisfies the inequality.
Testing the options Let's test each option:
A) x = 0 : Substituting x = 0 into the inequality, we get 0 − 6 ≥ − 7 , which simplifies to − 6 ≥ − 7 . This is true because -6 is greater than -7.
B) x = − 2 : Substituting x = − 2 into the inequality, we get − 2 − 6 ≥ − 7 , which simplifies to − 8 ≥ − 7 . This is false because -8 is less than -7.
C) x = − 7 : Substituting x = − 7 into the inequality, we get − 7 − 6 ≥ − 7 , which simplifies to − 13 ≥ − 7 . This is false because -13 is less than -7.
D) x = − 5 : Substituting x = − 5 into the inequality, we get − 5 − 6 ≥ − 7 , which simplifies to − 11 ≥ − 7 . This is false because -11 is less than -7.
Finding the solution Only option A, x = 0 , satisfies the inequality x − 6 ≥ − 7 .
Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, imagine you're managing a budget and need to ensure your expenses don't exceed your income. If your income is represented by x and your expenses are 6 , t h e n t h e in e q u a l i t y x - 6 \geq -7 co u l d re p rese n t a s i t u a t i o n w h ereyo u w an tt o d e t er min e t h e minim u min co m e ( x$) needed to cover your expenses while staying above a certain financial threshold (-7). Solving such inequalities helps in making informed financial decisions.
