Decide whether the two inequalities are equivalent. Explain. 21 < 7 - x; x < 14

A. Yes; if you solve the first inequality for x, you will end up with the second inequality.

B. No; if you graph both inequalities on the same number line, you will cover all real numbers.

C. No; if you graph both inequalities on the same graph, you will get x = 14.

D. No; if you solve the first inequality for x, you will end up with x < - 14, which is not equivalent to x < 14

Question

Mendoza

Mathematics

2 July, 05:52

Decide whether the two inequalities are equivalent. Explain. 21 < 7 - x; x < 14

A. Yes; if you solve the first inequality for x, you will end up with the second inequality.

B. No; if you graph both inequalities on the same number line, you will cover all real numbers.

C. No; if you graph both inequalities on the same graph, you will get x = 14.

D. No; if you solve the first inequality for x, you will end up with x < - 14, which is not equivalent to x < 14

+3

Answers (1)

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Randall Alexander · Answer 1

Given inequalities are 21 < 7 - x and x < 14

Now we have to decide whether the two inequalities are equivalent or not.

To find that first we need to simplify the given inequaity

21 < 7 - x

subtract 7 from both sides

21-7 < 7-x-7

14<-x

multiply both side by - 1

-14 > x (because multiplying or dividing some negative number flips the type of inequality)

or we can write x<-14

We can clearly see that x < - 14 and x<14 are not same.

Hence choice D is correct.