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chapter9.4b
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1994-01-28
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à 9.4 Translating a sentences into an Equation.
äïPlease translate the following written sentences and
solve.
âïTranslate and solve the following sentence.ï"Two times a
number added to eight is equal to eighteen."
êêêë2x + 8ï=ï18
èAdd -8 to both sides.ë -8ë-8
#êêêë─────────────
êêêë2xë =ï10
êêêë xë =ï5ëThe number is 5.
éSèTranslating a written sentence into an equation involves
changing words into symbols.ïIn order to translate, "Two times a
number added to eight is equal to eighteen," you should let "x"
represent the "number" and make the following translations.
êêë Two times a numberè...è2∙x
êêë added to eightê...è+ 8
êêë is equal toêè...è=
êêë eighteenêë ...è18
The translation is the equation, 2∙x + 8ï=ï18.ïOnce the equation is
translated, you can then solve it as was done in the last section.
êêêêêï2x + 8ï=ï18
êë Add -8 to both sides.ê-8ë-8
#êêêêêï─────────────
êêêêêï2xë =ï10
êè Multiply by 1/2.ê(1/2)∙2xï=ï(1/2)∙10
êêêêêë xï=ï5
Thus, the number described in the original sentence is 5.
ï1èTranslate and solve.
êë When three times a number is added to eighteen, the
êêresult is twenty-seven.
êèA)ï3êèB)ï-6êïC)ï2êèD)ïå
üêêêêï3x + 18ï=ï27
êë Add -18 to both sides.ë-18è -18
#êêêêê ──────────────
êêêêê 3xê=è9
êè Multiply by 1/3.ë (1/3)∙3xï=ï(1/3)∙9
êêêêêëxï=ï3
êêêè The number is 3.
ÇïA
ï2èTranslate and solve.
êë The sum of four times a number and six is equal to
êêtwenty-two.
êèA)ï4êèB)ï-6êïC)ï8êèD)ïå
üêêêêï4x + 6ï=ï22
êë Add -6 to both sides.ë -6ë-6
#êêêêê ──────────────
êêêêê 4xë =ï16
êè Multiply by 1/4.ë (1/4)∙4xï=ï(1/4)∙16
êêêêêëxï=ï4
êêêêêThe number is 4.
ÇïA
ï3èTranslate and solve.
êë If seven is subtracted from three times a number, the
êêresult is fifteen.
êêè2êë 1êê 1
#êèA)ï-5 ─êB)ï7 ─ê C)ï-9 ─êD)ïå
êêè3êë 3êê 3
üêêêêï3x - 7ï=ï15
êë Add 7 to both sides.ê 7ë 7
#êêêêê ──────────────
êêêêê 3xë =ï22
êè Multiply by 1/3.ë (1/3)∙3xï=ï(1/3)∙22
êêêêêëxï=ï22/3 or 7 1/3
ÇïB
ï4èTranslate and solve.
êë If five is subtracted from a number, the result is
êêminus twenty-three.
êèA)ï-24ê B)ï6êèC)ï-18ê D)ïå
üêêêêïx - 5ï=ï-23
êë Add 5 to both sides.ê5ê5
#êêêêê ──────────────
êêêêê xë =ï-18
êêêè The number is -18.
ÇïC
ï5èTranslate and solve.
êë If three times a number is subtracted from eighteen,
êêthe result is twenty-four.
êèA)ï-2êïB)ï-6êïC)ï12êïD)ïå
üêêêêè18 - 3xï=ï24
êëAdd -18 to both sides.ï-18êï-18
#êêêêêï──────────────
êêêêêë-3xï=ï6
êëMultiply by -1/3.è (-1/3)∙(-3x)ï=ï(-1/3)∙6
êêêêêïxï=ï-2
êêêêêïThe number is -2.
ÇïA