Chapter 3: Q.4 (page 156)

Are $- 2 x > 6$ and $x > - 3$ equivalent inequalities? Why or why not?

Short Answer

Expert verified

No, the inequalities are not equivalent due to reverse inequality concept comes.

Step by step solution

Step 1. Apply the concept of Linear inequalities

In this type of question, apply the concept of basic linear inequalities to get the equivalent by multiplying the number or dividing the numbers and also using the reverse inequality concept.

Step 2. Finding whether it is equivalent or not

Since, the expression is $- 2 x > 6$ .

Now, simply dividing $- 2$ to both side of the inequality, it gives

$\begin{array}{l} - 2 x > 6 \\ \frac{- 2 x}{- 2} > \frac{6}{- 2} \\ x < - 3 \end{array}$

The inequality $- 2 x > 6, x > - 3$ are not equivalent to each other.

Step 3. Reason for not the equivalency

Since, $- 2 x > 6$ & $x > - 3$ are not equivalent inequalities because when a negative number is multiplying or dividing on both side of the inequality it reverse the inequality sign and that differs the equivalency.

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Are $- 2 x > 6$ and $x > - 3$ equivalent inequalities? Why or why not?

Short Answer

Step by step solution

Step 1. Apply the concept of Linear inequalities

Step 2. Finding whether it is equivalent or not

Step 3. Reason for not the equivalency

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Are -2x>6 and x>-3 equivalent inequalities? Why or why not?

Short Answer

Step by step solution

Step 1. Apply the concept of Linear inequalities

Step 2. Finding whether it is equivalent or not

Step 3. Reason for not the equivalency

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Pure Maths

Mechanics Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Are $- 2 x > 6$ and $x > - 3$ equivalent inequalities? Why or why not?