What is the solution to this inequality?
[tex]$-16 x>-80$[/tex]
A. [tex]$x<-5$[/tex]
B. [tex]$x>5$[/tex]
C. [tex]$x>-5$[/tex]
D. [tex]$x<5$[/tex]
Answer (2)
Divide both sides of the inequality by -16, remembering to flip the inequality sign: x < − 16 − 80 .
Simplify the fraction: x < 5 .
The solution to the inequality is x < 5 .
The final answer is x < 5 .
Explanation
Analyzing the Inequality We are given the inequality -80"> − 16 x > − 80 . Our goal is to isolate x to find the solution.
Dividing by -16 To solve for x , we need to divide both sides of the inequality by − 16 . It's very important to remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign. So, dividing both sides by − 16 gives us: − 16 − 16 x < − 16 − 80
Simplifying the Inequality Now, let's simplify the inequality. On the left side, − 16 − 16 x simplifies to x . On the right side, − 16 − 80 simplifies to 5 because a negative number divided by a negative number is positive, and 80 ÷ 16 = 5 . Therefore, we have: x < 5
Final Answer So, the solution to the inequality -80"> − 16 x > − 80 is x < 5 . This corresponds to option D.
Examples
Imagine you're sharing a pizza with friends. If you have a rule that 'the number of slices you take multiplied by -16 must be greater than -80', this inequality helps you figure out the maximum number of slices you can take! Solving inequalities is useful in everyday situations where there are limits or constraints.
The solution to the inequality -80"> − 16 x > − 80 is x < 5 . Therefore, the correct option is D. By dividing by a negative number, we flipped the inequality sign from 'greater than' to 'less than'.
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