Heart of Algebra Lessons 1 & 2 Simplifying expressions and absolute value Evaluating expressions and formulas Writing expressions from sentences Solve Equations Literal Equations Solve Inequalities Absolute Value Equations and Inequalities

Simplifying expressions and absolute value Remember to only add “like terms” which includes all variables and matching exponents When multiplying a polynomial by a monomial remember to distribute When dividing a polynomial by a monomial remember to divide each piece by the monomial. It may be helpful to rewrite. Simplify inside the absolute value bars before applying the bars to the single number

Evaluating expressions and formulas If you are allowed a calculator, remember that negative numbers should be typed in parentheses. Do not push the minus sign for a negative number! When evaluating formulas be sure to chose the correct unit at the end of the problem Area is units squared Ex) cm2 Volume is units cubed Ex) ft3 Rates are unit per unit Ex) miles per hour

Writing expressions from sentences Know your key words Addition: sum, increased by, more Subtraction: difference, decreased by, less Three less than a number means to take 3 away! n – 3 Multiplication: product, times, twice, triple Division: quotient, divided by Watch for needed parentheses!

Solving Equations Distribute and simplify each side Move letters to one side (left) and move numbers to the other side (right) Divide or multiply to get the letter alone To move a fraction in front of the letter – multiply by the reciprocal Remember to multiply by a fraction you multiply by the numerator and divide by the denominator

Literal Equations To move an equation containing multiple letters around follow all the same rules of solving equations Move pieces in addition and subtraction first Move the pieces in multiplication or division last These include solving formulas for a different variable

Solving Inequalities Solve inequalities just like you solve equations If you multiply or divide BY a negative number for your last step remember to flip the inequality sign! Less than sign looks like an L that is tipped < Greater than sign does not look like an L > When graphing solutions remember that < and > use open circles because the answer is not included where as ≤ and ≥ use closed circles because the answer is included

Absolute Value Equations and Inequalities Absolute Value equations have two answers Isolate the absolute value before writing the two new equations 1st equation as is – drop bars 2nd equation – drop bars and make right side negative Solve absolute value inequalities like equations Flip the inequality symbol when writing the 2nd problem Less than problems make a single answer in the middle Greater than problems make two answers on the ends of the graph