Question

Your classmate says that the solutions to the given inequality are x > -2. Look carefully at the work. Should your friend have reversed the inequality​ symbol? Explain. Then solve the inequality correctly.

Please don't send those annoying files, I'm not trying to get a virus on my laptop. Please, if you can, just write out the steps/answer(s).

Answer 1

x < -2 (No, he shouldn't have reversed the inequality symbol).

Explanation:

Given the algebraic expression;

19 - 2(1 - x) < 13

Opening up the bracket, we have;

19 + (-2*1) + (-2*-x) < 13

19 + (-2) + (2x) < 13

19 - 2 + 2x < 13

17 + 2x < 13

Rearranging the equation, we have;

2x < 13 - 17

2x < -4

Dividing both sides by 2, we have;

x < -2

Hence, your friend shouldn't have reversed the inequality symbol (sign).

Note: you should only flip the inequality symbol (sign) when you're dividing by a negative number such as -2.

For example, if we had re-arranged the equation as;

17 - 13 < -2x

4 < -2x

Dividing both sides by -2, we have;

4 > x