Question

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Answer 1

Answer: $-\frac{3}{2} \leq x < 5$

Step-by-step explanation:

We can split this into two inequalities, namely $2x-3 < x+2$ and $x+2 \leq 3x+5$.

Solving the first inequality,

$2x-3 < x+2\\\\x-3 < 2\\\\x < 5$

Solving the second inequality,

$x+2 \leq 3x+5\\\\2 \leq 2x+5\\\\-3 \leq 2x\\\\-\frac{3}{2} \leq x$

So, the solution is $-\frac{3}{2} \leq x < 5$