Solving Equations and Inequalities 1-7 and 1-8 English Casbarro Unit 1 : Relations and Functions

Warm-up: Solve the following problems The sum of the angle measures of a triangle is 180°. Find the measure of each angle. (x – 1)° (5x – 3)° 3. Solve the formula for n. 4. Solve for x. 5. Solve the following system:

1-5: Solving Equations  The most important thin to remember is to “isolate” the variable.  Everything that has been done to the variable has to be “undone” by you. Ex. x + 5 = 8 [the only thing that has been done to x is add 5  to “undo” it, you will subtract 5 from both sides, to get x = 3]

All equations start with these basics, and then get more complicated. The good news is that you will use the same steps to solve problems no matter how complicated the problems get. All problems are the same!

Try these:

Literal Equations  These are equations where you are ending up with a new equation solved for a particular variable (like warm-up question #3)  You will still follow the rules of “undoing” everything to “isolate the variable” that you need.

A lot of the literal equations you are asked to solve will be formulas.

1-8: Solving Inequalities  If you know how to solve equations, you know how to solve inequalities.  The difference in the two is that a solution to an equation is one particular number; the solution to an inequality is a whole range of numbers.  Sometimes, you must graph the answer to an inequality on a number line.  If you multiply or divide an inequality by a negative sign, you must switch the inequality symbol.

After you have solved an inequality, you can graph the solution set as in the examples below.