Question

836*.
1)||2х+3|-2|=5
2)||3х-2|+3|=7
3)||4х+3|-5|=8

Answer 1

Ответ:

1) x∈{-5; 2}

2) x∈{-2/3; 2}

3) x∈{-4; 2,5}

Пошаговое объяснение:

Нужно знать:

$\displaystyle \tt 1) \; |a|=b \;(b>0) \Leftrightarrow \left [{ {{a=-b} \atop {a=b}} \right. \\\\2) \; |a|=b \;(b<0) \Leftrightarrow \varnothing\\\\3) \; |a|=0 \;(b=0) \Leftrightarrow a=0.$

Решение.

$\displaystyle \tt 1) \; ||2x+3|-2|=5 \Leftrightarrow \left [{ {{|2x+3|-2=-5 } \atop {|2x+3|-2=5}} \right. \Leftrightarrow \left [{ {{|2x+3|=-3 } \atop {|2x+3|=7}} \right. \Leftrightarrow \\\\\Leftrightarrow \left [{ {{\varnothing } \atop {|2x+3|=7}} \right. \Leftrightarrow |2x+3|=7 \Leftrightarrow \left [{ {{2x+3=-7 } \atop {2x+3=7}} \right. \Leftrightarrow \\\\ \Leftrightarrow \left [{ {{2x=-10} \atop {2x=4}} \right. \Leftrightarrow \left [{ {{x=-5} \atop {x=2}} \right..$

$\displaystyle \tt 2) \; ||3x-2|+3|=7 \Leftrightarrow \left [{ {{|3x-2|+3=-7 } \atop {|3x-2|+3=7}} \right. \Leftrightarrow \left [{ {{|3x-2|=-10} \atop {|3x-2|=4}} \right. \Leftrightarrow \\\\\Leftrightarrow \left [{ {{\varnothing } \atop {|3x-2|=4}} \right. \Leftrightarrow |3x-2|=4 \Leftrightarrow \left [{ {{3x-2=-4 } \atop {3x-2=4}} \right. \Leftrightarrow \\\\ \Leftrightarrow \left [{ {{3x=-2} \atop {3x=6}} \right. \Leftrightarrow \left [{ {{x=-\dfrac{2}{3} } \atop {x=2}} \right..$

$\displaystyle \tt 1) \; ||4x+3|-5|=8 \Leftrightarrow \left [{ {{|4x+3|-5=-8 } \atop {|4x+3|-5=8}} \right. \Leftrightarrow \left [{ {{|4x+3|=-3 } \atop {|4x+3|=13}} \right. \Leftrightarrow \\\\\Leftrightarrow \left [{ {{\varnothing } \atop {|4x+3|=13}} \right. \Leftrightarrow |4x+3|=13 \Leftrightarrow \left [{ {{4x+3=-13 } \atop {4x+3=13}} \right. \Leftrightarrow \\\\ \Leftrightarrow \left [{ {{4x=-16} \atop {4x=10}} \right. \Leftrightarrow \left [{ {{x=-4} \atop {x=2,5}} \right..$