$\\$
`6,`
`|b-8| +21=100`
`-> |b-8| = 100-21`
`-> |b-8|=79`
`->` \(\left[ \begin{array}{l}b-8=79\\b-8=-79\end{array} \right.\) $\\$ `->` \(\left[ \begin{array}{l}b=79+8\\b=-79+8\end{array} \right.\) $\\$ `->` \(\left[ \begin{array}{l}b=87\\b=-71\end{array} \right.\)
Vậy `b=87` hoặc `b=-71`
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`7,`
`|a+5| + |b-1/2|=0`
Với mọi `a,b` có : $\begin{cases} |a+5|≥0\\|b-\dfrac{1}{2}|≥0 \end{cases}$
`-> |a+5| + |b-1/2| ≥0∀a,b`
Dấu "`=`" xảy ra khi :
`↔` $\begin{cases} |a+5|=0\\|b-\dfrac{1}{2}|=0 \end{cases}$
`↔` $\begin{cases} a+5=0\\b-\dfrac{1}{2}=0 \end{cases}$
`↔` $\begin{cases} a=0-5\\b=0+\dfrac{1}{2} \end{cases}$
`↔` $\begin{cases} a=-5\\b=\dfrac{1}{2} \end{cases}$
Vậy `(a;b)=(-5; 1/2)`
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`8,`
`3 |a+1| - 4 = |a+1|`
`-> 3 |a+1| - 4 -|a+1|=0`
`-> (3|a+1| - |a+1|)-4=0`
`-> |a+1| (3-1) - 4=0`
`->2 |a+1| -4=0`
`-> 2 |a+1|=0+4`
`-> 2 |a+1|=4`
`->|a+1|=4:2`
`->|a+1|=2`
`->` \(\left[ \begin{array}{l}a+1=2\\a+1=-2\end{array} \right.\) $\\$ `->` \(\left[ \begin{array}{l}a=2-1\\a=-2-1\end{array} \right.\) $\\$ `->` \(\left[ \begin{array}{l}a=1\\a=-3\end{array} \right.\)
Vậy `a=1` hoặc `a=-3`
