Which solution value satisfies the inequality $x-6 \geq -7$?
A) $x=0$
B) $x=-2$
C) $x=-7$
D) $x=-5$
Answer (1)
Substitute each given value into the inequality x − 6 ≥ − 7 .
Check if the inequality holds true for each value.
x = 0 gives − 6 ≥ − 7 , which is true.
The solution that satisfies the inequality is x = 0 .
Explanation
Understanding the problem We are given the inequality x − 6 ≥ − 7 and four possible solutions. Our goal is to find which of the given values for x satisfies the inequality. We will substitute each value into the inequality and check if it holds true.
Testing each solution Let's test each option:
A) x = 0 : Substituting x = 0 into the inequality gives 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 gives − 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 gives − 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 gives − 5 − 6 ≥ − 7 , which simplifies to − 11 ≥ − 7 . This is false because -11 is less than -7.
Finding the solution Only x = 0 satisfies the inequality x − 6 ≥ − 7 . Therefore, the solution is x = 0 .
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 maximum allowable expenses are y , the inequality x ≥ y ensures you stay within your budget. Similarly, in manufacturing, tolerances are often specified using inequalities to ensure product quality. If a part's length must be within a certain range, inequalities define the acceptable limits, preventing defects and ensuring proper functionality.
