Heart of Algebra Lessons 1 2 Simplifying expressions

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) cm 2 – Volume is units cubed Ex) ft 3 – 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 – 1 st equation as is – drop bars – 2 nd equation – drop bars and make right side negative • Solve absolute value inequalities like equations • Flip the inequality symbol when writing the 2 nd problem – Less than problems make a single answer in the middle – Greater than problems make two answers on the ends of the graph