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English Senior High

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Mathematics Senior High

(2)がわからないです。x<2a+5はとけましたがそのあとが分かりません。6<2a+5<=7ってどういうことですか?

48 1次不等式の整数解 |基本 26 OC 基本例題 29 (1) 不等式 6x+8(4-x) > 5 を満たす2桁の自然数xをすべて求めよ。 (2) 不等式 5(x-1)<2(2x+α) を満たすxのうちで、最大の整数が6であ るとき,定数aの値の範囲を求めよ。 CHART OLUTION 1次不等式の整数解 数直線を利用 まずは、与えられた不等式を解く。 (1) 不等式の解で, 2桁の自然数であるものを求める。 (2) 不等式の解が,x<A の形となる。 ここで, x<Aを満たす最大の整数が 6であるということは, x=6 は x<A に含まれ るが, x=7 は x<A に含まれないということ。 これを図に示すと右のようになる。 解答 (1) 6x+8(4-x) >5 5 ≤7-2x>-27 27 ゆえに xは2桁の自然数であるから 10≦x≦13 x=10, 11, 12,13 よって x<- =13.5 のときである。 ゆえに よって 1/12kas よって2桁 1<2a≦2 14 10 11 12 1313.5 x 850 (2) 5(x-1)<2(2x+α) から x<2a+5.. ① ① を満たすxのうちで最大の整数が6となるのは 6<2a+5≤7 a+nE-< 6 A 7 x 6 2a+5 7 x ①を満たす最大の整数 200 連立不等式の 基本例 Aの箱の あり、こ でAの箱 た。最初 CHART OLUT 展開して整理。 不等号の向きが変わる。 - Sat ◆解の検討。 $300 SD AT 0-9 [S] ◆展開して整理。 ! 解答 最初, 6<2a+5<7 とか 6≦2a+5≦7 などとし ないように注意する。 A, 整理 Aの箱 A, 整 ①と xは した a=1のとき、不等式 7で、条件を満たす a=1のとき, 不等式 P

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