Question Number 55296 by Otchere Abdullai last updated on 20/Feb/19
$${simplify}\:{the}\:{following}\:{expression}\:{if} \\ $$$${x}<\mathrm{0} \\ $$$$\mid\mathrm{4}{x}−\sqrt{\left(\mathrm{3}{x}−\mathrm{1}\right)^{\mathrm{2}} }\mid \\ $$
Answered by mr W last updated on 20/Feb/19
$${with}\:{x}<\mathrm{0} \\ $$$$\Rightarrow\mathrm{3}{x}−\mathrm{1}<\mathrm{0} \\ $$$$\Rightarrow\mathrm{7}{x}−\mathrm{1}<\mathrm{0} \\ $$$$\mid\mathrm{4}{x}−\sqrt{\left(\mathrm{3}{x}−\mathrm{1}\right)^{\mathrm{2}} }\mid \\ $$$$=\mid\mathrm{4}{x}−\mid\mathrm{3}{x}−\mathrm{1}\mid\mid \\ $$$$=\mid\mathrm{4}{x}−\left(\mathrm{1}−\mathrm{3}{x}\right)\mid \\ $$$$=\mid\mathrm{7}{x}−\mathrm{1}\mid \\ $$$$=\mathrm{1}−\mathrm{7}{x} \\ $$
Commented by Otchere Abdullai last updated on 20/Feb/19
$${Thank}\:{You}\:{prof}\:{W} \\ $$