Question

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

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.