Question
Consider the following inequality:
Step 1 of 2 : Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.
Ask by Harrington Mcguire. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
To solve the inequality
for the variable
, follow these steps:
Step 1:
Subtract 4 from both sides of the inequality to isolate the term containing :
Subtract 4 from both sides of the inequality to isolate the term containing
Simplifying both sides:
Step 2:
Divide both sides by 3 to solve for :
Divide both sides by 3 to solve for
Final Answer:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
To solve the inequality
, we first isolate the term with
by subtracting 4 from both sides:
This simplifies to:
Next, we divide both sides by 3:
So, the solution in algebraic notation is
.
Now, let’s explore some additional knowledge related to inequalities.
Understanding inequalities can be a game-changer! They play a crucial role in various fields, from economics to engineering. For example, in optimization problems, using inequalities helps to define the limits within which a solution can be found, guiding decisions based on constraints to maximize resources effectively.
A common mistake when solving inequalities is forgetting that if you multiply or divide by a negative number, you must reverse the inequality sign. For instance, if you accidentally divided
by
without changing the direction of the inequality, you’d end up with an incorrect answer of
instead of the correct
. Always remember to keep an eye on that sign!