Question

Solve the following inequality
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Answer 1

$\text { The given inequality for real } x: 2(2 x+3)-10<6(x-2)\\\begin{array}{l}2(2 x+3)-10<6(x-2) \\4 x+6-10<6 x-12 \\4 x-6 x<-12+4 \\-2 x<-8 \\-x<\frac{-8}{2} \\-x<-4\end{array}$

$\text { Since } x \text { is negative, we multiply both sides by-1 \& change the signs }\\\begin{array}{l}(-1) \times(-x)>(-1) \times(-8) \\x>4\end{array}$

$\text { Since } x \text { is a real number which is greater than } 4\\\text { Hence, } x \in(4, \infty) \text { is the solution }$