Section 5.5 from Basic Mathematics Review by Oka Kurniawan was developed by OpenStax College, licensed by Rice University, and is available on the

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1 Section 5.5 from Bsic Mthemtics Review by Ok Kurniwn ws developed by OpenStx College, licensed by Rice University, nd vilble on the Connexions website. It used under Cretive Commons Attribution 3.0 Unported license.

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3 314 CHAPTER 5. SOLVING LINEAR EQUATIONS AND INEQUALITIES Trnslting from Verbl to Mthemticl Expressions To solve problem using lgebr, we must rst express the problem lgebriclly. To express problem lgebriclly, we must scrutinize the wording of the problem to determine the vribles nd constnts tht re present nd the reltionships mong them. Then we must trnslte the verbl phrses nd sttements to lgebric expressions nd equtions. To help us trnslte verbl expressions to mthemtics, we cn use the following tble s mthemtics dictionry. Word or Phrse Mthemtics Dictionry Mthemticl Opertion Sum, sum of, dded to, incresed by, more thn, plus, nd + Dierence, minus, subtrcted from, decresed by, less, less thn Product, the product of, of, muitiplied by, times Quotient, divided by, rtio Equls, equl to,, the result, becomes = A, n unknown quntity, n unknown, quntity Tble 5.1 x (or ny symbol) Smple Set A Trnslte the following phrses or sentences into mthemticl expressions or equtions. Exmple 5.28 Exmple 5.29 Exmple 5.30 Exmple 5.31 six more thn. 6 + x 6+x Fifteen minus. 15 x 15 x A quntity less eight. y 8 y 8 Twice ten. 2 x = 10 2x=10 Avilble for free t Connexions <

4 315 Exmple 5.32 Exmple 5.33 One hlf z of 1 2 = twenty z=20 Three times ve more thn twice the sme. 3 y = y 3y=5+2y Prctice Set A Trnslte the following phrses or sentences into mthemticl expressions or equtions. Exerce (Solution on p. 358.) Eleven more thn. Exerce (Solution on p. 358.) Nine minus. Exerce (Solution on p. 358.) A quntity less twenty. Exerce (Solution on p. 358.) Four times thirty two. Exerce (Solution on p. 358.) One third of six. Exerce (Solution on p. 358.) Ten times eight more thn ve times the sme. Sometimes the structure of the sentence indictes the use of grouping symbols Smple Set B Trnslte the following phrses or sentences into mthemticl expressions or equtions. Exmple 5.34 Comms set o terms. Exmple 5.35 A divided by ve, minus ten, ( x 5) 10 = fteen. 15 x 5 10=15 Eight divided by ve more thn ten 8 (5 + x) = 10 The wording indictes th to be considered s single quntity x = 10 Avilble for free t Connexions <

5 316 CHAPTER 5. SOLVING LINEAR EQUATIONS AND INEQUALITIES Exmple 5.36 A multiplied by ten more thn itself twenty. x (10 + x) = 20 x(10 + x) = 20 Exmple 5.37 A plus one divided by three times the minus twelve nd the result four. (x + 1) (3 x 12) = 4 x+1 3x 12 = 4 Notice tht since the phrse "three times the minus twelve" does not contin comm, we get the expression 3x 12. If the phrse hd ppered s "three times the, minus twelve," the result would hve been x + 1 3x 12 = 4 Exmple 5.38 Some phrses nd sentences do not trnslte directly. We must be creful to red them properly. The word from often ppers in such phrses nd sentences. The word from mens " point of deprture for motion." The following trnsltion will illustrte th use. The word from indictes the motion (subtrction) to begin t the point of "some quntity." Exmple 5.39 Eight less thn some quntity. Notice tht less thn could be replced with from. x Prctice Set B Trnslte the following phrses nd sentences into mthemticl expressions or equtions. Exerce (Solution on p. 358.) A divided by sixteen, plus one, ve. Exerce (Solution on p. 358.) Seven times two more thn twenty-one. Exerce (Solution on p. 358.) A divided by two more thn itself zero. Exerce (Solution on p. 358.) A minus ve divided by twice the plus three nd the result seventeen. Exerce (Solution on p. 358.) Fifty-two subtrcted from some quntity. Exerce (Solution on p. 358.) An unknown quntity subtrcted from eleven nd the result ve less thn the unknown quntity. Avilble for free t Connexions <

6 5.5.7 Exerces For the following problems, trnslte the following phrses or sentences into mthemticl expressions or equtions. Exerce (Solution on p. 358.) A quntity less four. Exerce Eight more thn. Exerce (Solution on p. 358.) A plus seven. Exerce A minus three. Exerce (Solution on p. 358.) Negtive ve plus n unknown quntity. Exerce Negtive sixteen minus some quntity. Exerce (Solution on p. 358.) Fourteen dded to twice. Exerce Ten dded to three times some. Exerce (Solution on p. 359.) One third minus n unknown quntity. Exerce Twice eleven. Exerce (Solution on p. 359.) Four ninths of twenty-one. Exerce One third of two fths. Exerce (Solution on p. 359.) Three times nine more thn twice the. Exerce Five times tht minus two. Exerce (Solution on p. 359.) Twice dded to six results in thirty. Exerce Ten times less four results in sixty-six. Exerce (Solution on p. 359.) A less twenty-ve equl to Exerce Seven more thn some ve more thn twice the. Exerce (Solution on p. 359.) When divided by four, the result sixty-eight. Exerce Eleven fteenths of two more thn eight. Exerce (Solution on p. 359.) One tenth of tht less one. 317 Avilble for free t Connexions <

7 318 CHAPTER 5. SOLVING LINEAR EQUATIONS AND INEQUALITIES Exerce Two more thn twice one hlf the less three. Exerce (Solution on p. 359.) A equl to itself plus four times itself. Exerce Three fths of quntity dded to the quntity itself thirty-nine. Exerce (Solution on p. 359.) A plus seven divided by two nd the result twenty-two. Exerce Ten times minus one divided by fourteen nd the result one. Exerce (Solution on p. 359.) A dded to itself then divided by three. Th result then divided by three. The entire result fteen. Exerce Ten divided by two more thn twenty-one. Exerce (Solution on p. 359.) Five divided by plus six fourteen. Exerce Twelve divided by twice fty-ve. Exerce (Solution on p. 359.) Twenty divided by eight times dded to one nine. Exerce A divided by itself, plus one, results in seven. Exerce (Solution on p. 359.) A divided by ten, plus four, results in twenty-four. Exerce A plus six, divided by two, seventy-one. Exerce (Solution on p. 359.) A plus six, divided by two, plus ve, forty-three. Exerce A multiplied by itself dded to ve thirty-one. Exerce (Solution on p. 359.) A quntity multiplied by seven plus twice itself ninety. Exerce A incresed by one nd then multiplied by ve times itself. The result eighty-four. Exerce (Solution on p. 359.) A dded to six nd tht result multiplied by thirteen. Th result then divided by six times the. The entire result equl to fty-nine. Exerce A subtrcted from ten nd tht result multiplied by four. Th result then divided by three more thn the. The entire result equl to six. Exerce (Solution on p. 359.) An unknown quntity decresed by eleven. Th result then divided by fteen. Now, one subtrcted from th result nd ve obtined. Exerce Ten less thn some. Avilble for free t Connexions <

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