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$\sf\displaystyle |2x+14|=6\\\left [{ {{2x+14=-6} \atop {2x+14=6}} \right. \left |{ {{x=-10} \atop {x=-4}} \right.$

Ответ: $-10;-4$

$\sf\displaystyle |9x-18|=27\\ \left [{ {{9x-18=-27} \atop {9x-18=27}} \right. \left [{ {{x=-1} \atop {x=5}} \right.$

Ответ: $-1;5$

$\sf\displaystyle |8x+12|=20\\\left [{ {{8x+12=-20} \atop {8x+12=20}} \right. \left [{ {{x=-4 } \atop {x=1}} \right.$

Ответ: $-4;1$

$\sf\displaystyle |15x-10|=5\\\left [{ {{15x-10=-5} \atop {15x-10=5}} \right. \left [{ {{x=\frac{1}{3}} \atop {x=1}} \right.$

Ответ: $\frac{1}{3};1$

$\sf\displaystyle |9x+15|=6\\\left [{ {{9x+15=-6} \atop {9x+15=6}} \right. \left [{ {{x=-\frac{21}{9} } \atop {x=-1}} \right. \left [{ {{x=-\frac{7}{3}} \atop {x=-1}} \right.$

Ответ: $-\frac{7}{3};-1$

$\sf\displaystyle |8x-6|=14\\\left [{ {{8x-6=-14} \atop {8x-6=14}} \right. \left [{ {{x=-1} \atop {x=2,5}} \right.$

Ответ: $-1;2,5$