Bài 15: Tìm x , Z, biết:
a) |x + 2| = 5
b) |x + 3| = 15
c) |x – 7| + 13 = 25
d) |x – 3| – 16 = – 4
e) 3 + x = 2
Bài 15: Tìm x , Z, biết:
a) |x + 2| = 5
b) |x + 3| = 15
c) |x – 7| + 13 = 25
d) |x – 3| – 16 = – 4
e) 3 + x = 2
Đáp án:
Giải thích các bước giải:
` Bài 15 : `
`a, | x+2 | = 5`
`<=> $\left \{ {{x+2=5} \atop {x+2=-5}} \right.$`
`<=> $\left \{ {{x=3} \atop {x=-7}} \right.$ `
`Vậy $\left \{ {{x=3} \atop {x=-7}} \right.$ `
` b, | x+3 | =15`
`<=> $\left \{ {{x+3=15} \atop {x+3=-15}} \right.$ `
`<=> $\left \{ {{x=5} \atop {x=-18}} \right.$ `
` Vậy $\left \{ {{x=5} \atop {x=-18}} \right.$ `
`c, |x – 7| + 13 = 25`
`<=> |x – 7| = 12`
`<=> $\left \{ {{x-7=12} \atop {x-7=-12}} \right.$`
`<=> $\left \{ {{x=19} \atop {x=-5}} \right.$ `
` Vậy $\left \{ {{x=19} \atop {x=-5}} \right.$ `
`d) |x – 3| – 16 = – 4`
` |x – 3| = 12 `
`<=> $\left \{ {{x-3=12} \atop {x-3=-12}} \right.$ `
`<=> $\left \{ {{x=15} \atop {x=-9}} \right.$ `
` Vậy $\left \{ {{x=15} \atop {x=-9}} \right.$ `
`e, 3 + x = 2`
`<=> x=2-3`
`<=> x = -1 `
`Vậy x=-1`
`a) |x + 2| = 5`
`<=>`\(\left[ \begin{array}{l}x+2=5\\x+2=-5\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-7\end{array} \right.\)
Vậy `x ∈ {3,-7}`
`b) |x + 3| = 15`
`<=>`\(\left[ \begin{array}{l}x +3=15\\x + 3=-15\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=12\\x=-18\end{array} \right.\)
Vậy `x ∈ {12,-18}`
`c) | x-7| + 13 = 25`
`<=>|x-7|=25-13`
`<=>|x-7|=12`
`<=>`\(\left[ \begin{array}{l}x-7=12\\x-7=-12\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=19\\x=-5\end{array} \right.\)
Vậy `x ∈ {19,-5}`
`d) |x-3| – 16 = – 4`
`<=> |x-3|=-4+16`
`<=>|x-3|=12`
`<=>`\(\left[ \begin{array}{l}x-3=12\\x-3=-12\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=15\\x=-9\end{array} \right.\)
Vậy `x ∈ {15,-9}`
`e) 3 + x = 2`
`<=>x=2-3`
`<=>x=-1`
Vậy `x ∈ {-1}`