解不等式组 $3x-1<2x+3\le7+5x$ 。

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完整解法

1. Split the compound inequality into two inequalities.

$3x-1<2x+3\le 7+5x$

This means

$3x-1<2x+3$ and $2x+3\le 7+5x$ .

2. Solve the left inequality.

$3x-1<2x+3$

$3x-2x<3+1$

$x<4$

3. Solve the right inequality and combine both results.

$2x+3\le 7+5x$

$2x-5x\le 7-3$

$-3x\le 4$

Dividing by $-3$ reverses the inequality sign:

$x\ge -\dfrac{4}{3}$

Combining with $x<4$ ,

$-\dfrac{4}{3}\le x<4$ .

答案

$-\dfrac{4}{3}\le x<4$

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