Solve each of the following inequalities for the given variable. Represent your solutions on a number line.  

1. $5+3x<5$ 

   Answer (a):

   $x<0$

   

2. $−3x\ge8−x$ 

   Hint (b):

   When you divide both sides of an inequality by a negative number,
   it reverses or 'flips' the sign. Here is an example of why that works:

   true statement $−3<5$
   multiply both sides by $−1−1·−3<5·−1$
   statement is no longer true $3<−5$
   reverse the inequality sign to make it true $3>−5$
   
   This also works with division by a negative number.

   Step 1(b):

   Add $x$ to both sides.

   $−2x\ge8$

   Step 2(b):

   Divide both sides by $−2$.

   Answer (b):

   $x\le−4$
   Did you remember to reverse the inequality sign?

   $\frac{-2x}{-2}\ge \frac{8}{-2}$