UNIT 1 HANDS ON EQUATIONS Final Exam Review

UNIT 1: HANDS ON EQUATIONS Final Exam Review

TOPICS TO INCLUDE v. Solving 2 -step equations v. Solving multi-step equations v. Equations with Negatives v. Distributive Property v. Vocabulary and Math Sentences v. Word Problems

SOLVING 2 -STEP EQUATIONS v. The goal of solving equations is to get the variable BY ITSELF v. To do this, you will need to first ADD or SUBTRACT, and then MULTIPLY or DIVIDE v. Example: 4 x – 2 = 10 Add 2 4 x = 12 Divide by 4 x=3

SOLVING 2 -STEP EQUATIONS v. You Try! 1. 2 x + 3 = 15 2. 9 x – 1 = 8

SOLVING MULTI-STEP EQUATIONS v. Always start by COMBINING LIKE TERMS on either side of the EQUALS SIGN v. Example: 4 x – x + 5 = 2 x – 4 + 15 Combine like terms 3 x + 5 = 2 x + 11 Subtract 5 3 x = 2 x + 6 Subtract 2 x x=6

SOLVING MULTI-STEP EQUATIONS v. You Try! 1. 2 x + 4 x – 5 = 4 x + 12 – 3 2. 5 x + 2 – 9 = 3 x + x – 7 + 3

EQUATIONS WITH NEGATIVES v. When solving equations, be careful with the NEGATIVES! v. A negative in front of a positive, will be NEGATIVE v. Example: -5(3 x) = -15 x v. A negative in front of a negative, will be POSITIVE v. Example: -2(-4 x) = 6 x v. EXAMPLE: Multiply -3 Add x Subtract 5 Divide by -5 or 4 – (-3) = 4+3 = 7 -3(2 x) + 5 = -x – 10 -6 x + 5 = -x – 10 -5 x + 5 = -10 -5 x = -15 x=3

EQUATIONS WITH NEGATIVES v. You Try! 1. -2(5 x) – 20 = 5 x – (-10) 2) + x 2. x – 4 + (-3 x) = 3 – (-

DISTRIBUTIVE PROPERTY v. Use the Distributive Property when there is a number being MULTIPLIED by a polynomial. v. Make sure you multiply the number by ALL TERMS in the polynomial. v. Then you can COMBINE LIKE TERMS and solve for x. v. Example: 2(x – 5) + 2 = 12 Distribute 2 x – 10 + 2 = 12 Combine like terms 2 x – 8 = 12 Add 8 2 x = 20 Divide by 2 x = 10

DISTRIBUTIVE PROPERTY v. You Try! 1. 3(x + 2) – 4 = 9 2. 4(3 x – 1) = 5(x + 3) – 5

VOCABULARY AND MATH SENTENCES v. Mathematical operations can be expressed by several difference vocabulary words. v. For example, INCREASED BY means ADDITION and PRODUCT means MULTIPLICATION v. You are going to practice writing mathematical sentences as expressions and vice versa.

VOCABULARY AND MATH SENTENCES v. Example: A number subtracted by eleven x – 11 v. Example: 3 x + 4 = 12 Three times a number plus four is twelve

VOCABULARY AND MATH SENTENCES v. You Try! Write each sentence as an expression 1. The sum of five and a number 2. The product of six and a variable 3. Seven subtracted by a number is nine 4. Four times a number minus one is seventy

VOCABULARY AND MATH SENTENCES v. You Try! Write each expression as a sentence 1. 5 x – 2 2. x + 13 = 4 3. x – 8 = 2 x + 1 4. 3(x – 1) = 9

WORD PROBLEMS v. Being able to solve word problems in math is very important. v. It is the closest you will come to REAL-WORLD APPLICATION Example: If three is added to twice a number, the result is 17. What is the number? 3 + 2 x = 17 2 x – 14 x=7

WORD PROBLEMS v. You Try! 1. Three times a number, increased by one is twentyfive. What is the number? 2. Four times a number, plus three is equal to twice the number, increased by nine. What is the number?

ALL DONE