ANSWER and EXPLANATION
a. The first inequality given is:
[tex]2x<-4[/tex]To solve this, divide both sides of the inequality by 2:
[tex]\begin{gathered} \frac{2x}{2}<-\frac{4}{2} \\ x<-2 \end{gathered}[/tex]To justify this, pick any number less than -2 and substitute it back into the original inequality:
Let x be -4:
[tex]\begin{gathered} 2(-4)<-4 \\ \Rightarrow-8<-4 \end{gathered}[/tex]As we can see, it is correct.
b. The second inequality given is:
[tex]-2x<4[/tex]To solve this, divide both sides by -2. The sign changes from < to > because we are dividing both sides by a negative number.
Therefore:
[tex]\begin{gathered} x>\frac{4}{-2} \\ x>-2 \end{gathered}[/tex]To justify this, pick any number greater than -2 and substitute it back into the original inequality:
Let x be -1:
[tex]\begin{gathered} -2(-1)<4 \\ 2<4 \end{gathered}[/tex]As we can see, it is correct.
The only challenge with solving the second inequality (-2x < 4) is that we have to change the sign form less than (<) to greater than (>) due to the division by a negative number.
