Solving Inequalities

Solving an inequality is finding the solutions to the variables.

Use the information below to help or go to this link: http://www.mathsisfun.com/algebra/inequality-solving.html 

Using substitution for solving inequalities is taking different numbers and plugging them into the variable to see if they work.

                                                            x-2>5

When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality. On the other hand, substituting -2 for x yields the false statement (-2)-2 > 5. Thus x = -2 is NOT a solution of the inequality. Inequalities usually have many solutions.

When solving equations with multiple variables, first solve for one then plug that answer in to the equation to solve for the other variable.

1. Problem: Solve the following system:          

  x + y = 11           

 3x - y = 5             

 Solution: Solve the first equation for y            

(you could solve for x - it doesn't matter).                      

 y = 11 - x <-- minus x from both sides to make it switch sides

Now, substitute 11 - x for y in the second equation.

This gives the equation one variable,

which earlier algebra work has taught 

you how to do.                         

3x - (11 - x) = 5 <-- take what the answer from above and put it into the second equation

3x - 11 + x = 5  <-- take the parenthesis out by distributing the minus through the parenthesis    

4x = 16 <-- add like terms to get this          

 x = 4 <--to get here divide both sides by 4

 Now, substitute 4 for x in either equation and solve for y.            

(We use the first equation below.)                        

 4 + y = 11 <-- plug 4 into the first equation again and solve to get y

  y = 7                        

 The solution is the ordered pair,            

 (4, 7) <--to get this take the x and y answers you got above and put them in order like you were going to graph it