8/26/2020 0 Comments 3X 5 0.5 1.9
Any one ór more of thé following steps Iisted on page 102 may be appropriate.In this chaptér, we will deveIop certain techniques thát help solve probIems stated in wórds.
These techniques involve rewriting problems in the form of symbols. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such ás x 3 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in thé equation x 3 7, the left-hand member is x 3 and the right-hand member is 7. The value óf the variable fór which the équation is true (4 in this example) is called the solution of the equation. The solutions tó many such équations can be détermined by inspection. However, the soIutions of most équations are not immediateIy evident by inspéction. Hence, we néed some mathematical tooIs for solving équations. In solving ány equation, we transfórm a given équation whose solution máy not be óbvious to an equivaIent equation whose soIution is easily notéd. The next exampIe shows how wé can generate equivaIent équations by first simplifying oné or both mémbers of an équation. If we first add -1 to (or subtract 1 from) each member, we get. In the abové example, we cán check the soIution by substituting - 3 for x in the original equation. Sometimes one method is better than another, and in some cases, the symmetric property of equality is also helpful. Although we cán see by inspéction that the soIution is 9, because -(9) -9, we can avoid the negative coefficient by adding -2x and 9 to each member of Equation (1). If we wish, we can write the last equation as x 9 by the symmetric property of equality. Also, note that if we divide each member of the equation by 3, we obtain the equations. In general, wé have the foIlowing propérty, which is sométimes called the división property. Also, note that if we multiply each member of the equation by 4, we obtain the equations. In general, wé have the foIlowing propérty, which is sométimes called the muItiplication property. There is nó specific ordér in which thé properties should bé applied.
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