W ARM U P 1. If a = 11 and b = 22 find [3(a + b) – 3a] 2. Simplify x 2 ÷ 4 Submit when finished.

L ESSON 1.3 THRU 5 E QUATIONS AND TRANSLATING WORDS INTO EQUATIONS Objective: 1.To find the solution set of equations over a given domain. 2. To translate phrases into variable expressions 3. To translate word sentences into equations

E QUATIONS An Equation is two expressions joined by an equal sign. If the equation has one or more variables it is called an open sentence Open sentences can have one solution, more than one solution or no solutions Solutions are called the of the equation. All the solutions form the solution set and are put in { }

E QUATIONS The domain of the variable is all the numbers that can be chosen from (ex: the set of real numbers) Ex: solve x + 4 = 11 if the domain for x is {1,3,5,7,11}

E QUATIONS Solve 2x – 5 = 13 if x  {3,6,9,12} is an element of

E QUATIONS Solve the equation m(3 –m) = 2 if m  { 0,1,2,3}

E QUATIONS Solve each equation if x  {0,1,2,3,4,5,6} 1. x + 6 = – x = x = ÷ x = 8

T RANSLATING W ORDS INTO S YMBOLS Phrases in English contain no verb, therefore mathematical phrases contain no equal or inequality sign. What words can be translated into mathematical operations?

T RANSLATING W ORDS INTO S YMBOLS Four times a number One half a number Eight more than twice a number Six less than a number

T RANSLATING S ENTENCES INTO E QUATIONS What part of speech is “is” in a sentence?

T RANSLATING S ENTENCES INTO E QUATIONS The verb of the sentence is the = in an equation. The sum of a number and 12 is equal to 78. n + 12 = 78

T RANSLATING S ENTENCES INTO E QUATIONS If a number is decreased by 5 and the result is multiplied by 2, then the result is 26. 2(x – 5) = 26

T RANSLATING S ENTENCES INTO E QUATIONS Three less the number x equals – x = 44

T RANSLATING S ENTENCES INTO E QUATIONS Eight more than a number is 25. Seven subtracted from a number is 9. Twice a number which is decreased by 7 is 35. Twice a number decreased by seven is 35.