Đáp án:
`1)` `x={14}/5`
`3)` `x={-9}/{46}`
`7)` `x\in {-1;1}`
`8)` `x={10}/3`
`9)` `x={-23}/5`
`10)` `x=13`
`12)` `x=5`
`13)` `x=-4`
`14)` `x\in {{-1}/{35};{-13}/{35}}`
`15)` `x=2`
Giải thích các bước giải:
`1)` `{15}/8-1/8 : (x/4-0,5)=5/4`
`=>1/8 : (x/4-0,5)={15}/8-5/4`
`=>1/8 : (x/4-1/2)=5/8`
`=>x/4-1/2=1/8 : 5/8`
`=>x/4-1/2=1/5`
`=>x/4=1/5+1/2`
`=>x/4=7/{10}`
`=>x=7/{10} . 4`
`=>x={14}/5`
Vậy `x={14}/5`
$\\$
`3)` `-2x-2/3 (3/4-1/8x)=(-1/2)^3`
`=> -2x-(1/2-3/4x)=-1/8`
`=>-2x-1/2+1/{12}x=-1/8`
`=>-2x+1/{12}x=-1/8+1/2`
`=>(-2+1/{12})x=-1/8+4/8`
`=>-{23}/{12} x=3/8`
`=>x=3/8 : (-{23}/{12})`
`=>x=3/8 . {-12}/{23}`
`=>x={-9}/{46}`
Vậy `x={-9}/{46}`
$\\$
`7)` `|x-2|-|1-2x|=0`
`=>|x-2|=|1-2x|`
`=>`$\left[\begin{array}{l}x-2=1-2x\\x-2=2x-1\end{array}\right.$
`=>`$\left[\begin{array}{l}x+2x=1+2\\x-2x=-1+2\end{array}\right.$
`=>`$\left[\begin{array}{l}3x=3\\-x=1\end{array}\right.$
`=>`$\left[\begin{array}{l}x=1\\x=-1\end{array}\right.$
Vậy `x\in {-1;1}`
$\\$
`8)` `1/{12}:4/{21}=3\ 1/2 :(3x-2)`
`=>1/{12}. {21}/4=7/2:(3x-2)`
`=>7/{16}=7/2 :(3x-2)`
`=>3x-2=7/2 : 7/{16}`
`=>3x-2=7/2 . {16}/7`
`=>3x-2=8`
`=>3x=8+2`
`=>3x=10`
`=>x={10}/3`
Vậy `x={10}/3`
$\\$
`9)` `8/{x-5}=3/{x+1}` `(x\ne 5; -1}`
`=>8(x+1)=3(x-5)`
`=>8x+8=3x-15`
`=>8x-3x=-15-8`
`=>5x=-23`
`=>x={-23}/5\ (thỏa\ điều kiện)`
Vậy `x={-23}/5`
$\\$
`10)` `{x-1}/{x+2}=4/5` `(x\ne -2)`
`=>5(x-1)=4(x+2)`
`=>5x-5=4x+8`
`=>5x-4x=8+5`
`=>x=13\ (thỏa\ điều kiện)`
Vậy `x=13`
$\\$
`12)` `2.3^x-405=3^{x-1}`
`=>2.3. 3^{x-1}-3^{x-1}=405`
`=>6.3^{x-1}-3^{x-1}=405`
`=>5.3^{x-1}=405`
`=>3^{x-1}={405}/5`
`=>3^{x-1}=81=3^4`
`=>x-1=4`
`=>x=4+1`
`=>x=5`
Vậy `x=5`
$\\$
`13)` `(3/4)^x={2^8}/{3^4}`
`=>(3/4)^x={(2^2)^4}/{3^4}`
`=>{3^x}/{4^x}={4^4}/{3^4}`
`=>3^x . 3^4=4^x . 4^4`
`=>3^{x+4}=4^{x+4}`
`=>x+4=0`
`=>x=-4`
Vậy `x=-4`
$\\$
`14)` `(5x+1)^2={36}/{49}`
`=>(5x+1)^2=(6/7)^2=(-6/7)^2`
`=>`$\left[\begin{array}{l}5x+1=\dfrac{6}{7}\\5x+1=\dfrac{-6}{7}\end{array}\right.$
`=>`$\left[\begin{array}{l}5x=\dfrac{6}{7}-1\\5x=\dfrac{-6}{7}-1\end{array}\right.$
`=>`$\left[\begin{array}{l}5x=\dfrac{-1}{7}\\5x=\dfrac{-13}{7}\end{array}\right.$
`=>`$\left[\begin{array}{l}x=\dfrac{-1}{35}\\x=\dfrac{-13}{35}\end{array}\right.$
Vậy `x\in {{-1}/{35};{-13}/{35}}`
$\\$
`15)` `[(-0,5)^3]^x=1/{64}`
`=>[(-1/2)^3]^x=1/{64}`
`=>(-1/8)^x=(-1/8)^2`
`=>x=2`
Vậy `x=2`
