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卡片上的数字为

m

, 则使关于

x

的方程

\frac{2}{x-1}+\frac{x+8}{1-x}-2

的解为正数, 且不等式组 $\left\...

Mar 9, 2024

卡片上的数字为

m

, 则使关于

x

的方程

\frac{2}{x-1}+\frac{x+8}{1-x}-2

的解为正数, 且不等式组

\left\{\begin{array}{l}2 x+3&gt;5 \\ x-m&lt;0\end{array}\right.

无解的楬事是_.

Solution by Steps

step 1

Solve the inequality \frac{2}{x-1}+\frac{x+8}{1-x}-2>0 for

x

step 2

The solution to the inequality is -4/3<x<1

step 3

Solve the system of inequalities \{2x+3>5, x-m<0\} for

m

step 4

The solution to the system is m>x and x>1

step 5

Combine the solutions from steps 2 and 4 to find the value of

m

that makes the equation's solution positive and the system of inequalities have no solution

step 6

Since

x

must be greater than

1

from the system of inequalities and less than

1

from the inequality, there is no overlap, hence no solution for

x

step 7

Therefore, any

m

greater than

1

will satisfy the condition that the system of inequalities has no solution

Answer

m>1

Key Concept

Combining solutions of inequalities

Explanation

The value of

m

must be chosen such that it satisfies the condition from the system of inequalities while also ensuring that the solution to the equation is positive. By combining the solutions, we find that

m

must be greater than

1