Maths problem: how to do (b), thanks?

2020-10-02 7:35 pm

回答 (1)

2020-10-02 8:50 pm
✔ 最佳答案
(a) (x-1)/3 ≦ (3x-1)/2 - 8
Sol.: 
(x-1)/3 ≦ (3x-1)/2 - 8
iff. 2(x-1) ≦ 3(3x-1) - 48
iff. 2x-2 ≦ 9x-3-48
iff. 9x-2x ≧ 48+3-2
iff. 7x ≧ 49
iff. x ≧ 7

(b) [(5-3x)/4 -1]/3 ≦ [3 (5-3x)/4- 1]/2 - 8
Sol.:
Let t = (5x-3)/4.
Then, the inequality becomes
    (t-1)/3 ≦ (3t-1)/2 - 48.
Hence, t ≧ 7.
That is (5-3x)/4 ≧ 7.
So, 5-3x ≧ 28.
Thus, the solution is x ≦ (5-28)/3 = -23/3.
 


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