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 byOtchere Abdullai last updated on 20/Feb/19
$${Thank}\:{You}\:{prof}\:{W} \\ $$