Which inequality graph is the solution to $x / 3<-2$?
A)
B) $-\sqrt{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1012345678910}$
C) $-109 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1012345678910$
D)
Answer (2)
We have the inequality x /3 < − 2 .
Multiply both sides by 3 to isolate x : x < − 6 .
The solution is all values of x less than -6.
The correct graph representing this solution is A.
Explanation
Understanding the Problem We are given the inequality x /3 < − 2 . Our goal is to solve for x and then identify the graph that represents the solution.
Solving the Inequality To solve the inequality, we need to isolate x . We can do this by multiplying both sides of the inequality by 3. This gives us:
x /3 < − 2 3 × ( x /3 ) < 3 × ( − 2 ) x < − 6
Interpreting the Solution The solution to the inequality is x < − 6 . This means that x can be any number less than -6, but not equal to -6. On a number line, this is represented by an open circle at -6 and an arrow extending to the left, indicating all numbers less than -6.
Identifying the Correct Graph Now, we need to identify which of the given options represents this solution. Option A is the correct graph, as it shows an open circle at -6 and an arrow extending to the left.
Final Answer Therefore, the correct answer is A.
Examples
Understanding inequalities like x /3 < − 2 is crucial in many real-world scenarios. For instance, imagine you're managing a budget where your expenses ( x ) divided by 3 must be less than -2 to avoid debt. Solving this inequality helps you determine the maximum amount you can spend. Similarly, in engineering, such inequalities can help define safety limits or acceptable ranges for measurements, ensuring systems operate within specified constraints.
The inequality 3 x < − 2 simplifies to x < − 6 . The correct graph showing all values less than − 6 is Option A, which has an open circle at − 6 and an arrow to the left. Therefore, the answer is A.
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