A student simplifies the inequality [tex]7 t-6\ \textgreater \ -5[/tex] to [tex]7 t\ \textgreater \ 1[/tex]. Which step did the student perform?
A. Multiplied both sides of the inequality by 7
B. Divided both sides of the inequality by 7
C. Added 6 to each side of the inequality
D. Subtracted [tex]7 t[/tex] from each side of the inequality
Answer (1)
Start with the initial inequality: -5"> 7 t − 6 > − 5 .
Add 6 to both sides: -5 + 6"> 7 t − 6 + 6 > − 5 + 6 .
Simplify the inequality: 1"> 7 t > 1 .
The student added 6 to each side of the inequality.
Explanation
Understanding the Problem We are given the inequality -5"> 7 t − 6 > − 5 and we want to find out what step was performed to get to the inequality 1"> 7 t > 1 .
Isolating the variable term To isolate the term with t , we need to get rid of the − 6 on the left side of the inequality. The opposite operation of subtracting 6 is adding 6. So, we add 6 to both sides of the inequality: -5 + 6"> 7 t − 6 + 6 > − 5 + 6
Simplifying the inequality Simplifying both sides, we get: 1"> 7 t > 1
Identifying the correct step Comparing this to the answer choices, we see that the student added 6 to each side of the inequality.
Final Answer Therefore, the student added 6 to each side of the inequality.
Examples
Understanding how to solve inequalities is crucial in many real-world scenarios. For instance, imagine you're trying to save money. If you need to have more than $500 in your account by the end of the month, and you start with $50, you can use inequalities to determine how much you need to save each day. Similarly, in cooking, if a recipe requires a certain temperature range, inequalities help ensure your oven is set correctly. These skills are also vital in fields like engineering, where tolerances and limits are often defined using inequalities.
