Question

Given: x + 3.8 > -10.02.

Choose the solution set.
a. {x | x ∈ R, x > -6.22}
b. {x | x ∈ R, x > -10.40}
c. {x | x ∈ R, x > -13.82}

Answer 1

So, we originally have our inequality:

x + 3.8 > -10.02.

In terms of addition, subtraction and multiplication across by a positive number, we can treat this inequality just like and equation (with an '=' sign), which you might be more familiar with. The solution set is the list of all the values which x can take on such that the equation is still satisfied (i.e. the left-hand side is less than the right-hand side). So, we can find this be getting x on its own, meaning that we subtract 3.8 from both sides of the inequality. This leaves us with:

x > -10.02 - 3.8

and if you work out the right-hand side here you should get an expression for x which provides the solution set. Hope that helps! :)

Answer 2

I got 13.82 so my answer is c? thank you for helping

Answer 3

Apologies, when I went to define what a solution set is I meant say it is the list of all the values which x can take on such that the INEQUALITY is still satisfied!

Yes, you've got it out @heathermae2373 ; x > -13.82 is the answer, so (c.) is correct. Hope you were able to follow it! :)