Đáp án:
Áp dụng tính chất:`|P|>=P,|P|>=-P`
`=>{(|x+2|>=-x-2),(|x+12|>=x+12):}`
`=>|x+2|+|x+12|>=-x-2+x+12=10`
Tương tự ta có:
`|x+3|+|x+10|>=-x-3+x+10=7`
`|x+4|+|x+9|>=-x-4+x+9=5`
`|x+5|+|x+8|>=-x-5+x+8=3`
`|x+6|+|x+7|>=-x-6+x+7=1`
`=>|x+2|+|x+3|+|x+4|+⋯+|x+10|+|x+12|>=10+7+5+3+1`
`=>|x+2|+|x+3|+|x+4|+⋯+|x+10|+|x+12|>=26`
Dấu "=" xảy ra khi `{({(x+2<=0),(x+12>=0):}),({(x+3<=0),(x+10>=0):}),({(x+4<=0),(x+9>=0):}),({(x+5<=0),(x+8>=0):}),({(x+6<=0),(x+7>=0):}):}`
`<=>{({(x<=-2),(x>=-12):}),({(x<=-3),(x>=-10):}),({(x<=-4),(x>=-9):}),({(x<=-5),(x>=-8):}),({(x<=-6),(x>=-7):}):}`
`<=>-6<=x<=7`
