Question

1. (4x + 3 < x < 6+9x)

Explanation:

Step1: Split the compound - inequality

Split $4x + 3

Step2: Solve $4x + 3

Subtract $4x$ from both sides: $3

Step3: Solve $x<6 + 9x$

Subtract $9x$ from both sides: $x-9x<6$, so $-8x<6$. Divide both sides by - 8 and reverse the inequality sign, we get $x>-\frac{3}{4}$.

Since $x<-1$ and $x>-\frac{3}{4}$ have no intersection, the solution set is the empty - set $\varnothing$.

Answer:

$\varnothing$