Question

a) |x − 3| − 16 = −4

b) 26 - |x + 9| = −13

c) 5 – ( 10 – x) = 7

d) 11 + ( 15 –x) = 1

e) 8x – 75 = 5x + 21

f) 9x + 25 = - ( 2x – 58)

g) |x + 3| = 4

h) 15 - |2x − 1| = |−8|

Answer 1

a, \(\left|x-3\right|-16=-4\Leftrightarrow\left|x-3\right|=12\)

\(\Leftrightarrow\orbr{\begin{cases}x-3=12\\x-3=-12\end{cases}\Leftrightarrow\orbr{\begin{cases}x=15\\x=-9\end{cases}}}\)

b, \(26-\left|x+9\right|=-13\Leftrightarrow\left|x+9\right|=39\)

\(\Leftrightarrow\orbr{\begin{cases}x+9=39\\x+9=-39\end{cases}\Leftrightarrow\orbr{\begin{cases}x=30\\x=-48\end{cases}}}\)

f, \(9x+25=-\left(2x-58\right)\Leftrightarrow9x+25=-2x+58\)

\(\Leftrightarrow11x-33=0\Leftrightarrow x=3\)

Làm nốt nhé ! 

Answer 2

a. \(\left|x-3\right|-16=-4\)

\(\Rightarrow\left|x-3\right|=12\)

\(\Rightarrow\orbr{\begin{cases}x-3=12\\x-3=-12\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=15\\x=-9\end{cases}}\)

b. \(26-\left|x+9\right|=-13\)

\(\Rightarrow\left|x+9\right|=39\)

\(\Rightarrow\orbr{\begin{cases}x+9=39\\x+9=-39\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=30\\x=-48\end{cases}}\)

c. \(5-\left(10-x\right)=7\)

\(\Rightarrow10-x=-2\)

\(\Rightarrow x=12\)

d. \(11+\left(15-x\right)=1\)

\(\Rightarrow15-x=-10\)

\(\Rightarrow x=25\)

e. \(8x-75=5x+21\)

\(\Rightarrow8x-5x=75+21\)

\(\Rightarrow3x=96\)

\(\Rightarrow x=32\)

f. \(9x+25=-\left(2x-58\right)\)

\(\Rightarrow9x+25=-2x+58\)

\(\Rightarrow9x+2x=58-25\)

\(\Rightarrow11x=33\)

\(\Rightarrow x=3\)

g. \(\left|x+3\right|=4\)

\(\Rightarrow\orbr{\begin{cases}x+3=4\\x+3=-4\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x=-7\end{cases}}\)

h. \(15-\left|2x-1\right|=\left|-8\right|\)

\(\Rightarrow15-\left|2x-1\right|=8\)

\(\Rightarrow\left|2x-1\right|=7\)

\(\Rightarrow\orbr{\begin{cases}2x-1=7\\2x-1=-7\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=4\\x=-4\end{cases}}\)

Answer 3

a,\(|x-3|-16=-4\)

\(< =>|x-3|=-4+16\)

\(< =>|x-3|=12\)

\(< =>\orbr{\begin{cases}x-3=12\\x-3=-12\end{cases}< =>\orbr{\begin{cases}x=15\\x=-9\end{cases}}}\)

b, \(26-|x+9|=-13\)

\(< =>-|x+9|=-13-26\)

\(< =>|x+9|=39\)

\(< =>\orbr{\begin{cases}x+9=39\\x+9=-39\end{cases}< =>\orbr{\begin{cases}x=30\\x=-48\end{cases}}}\)

c, \(5-\left(10-x\right)=7\)

\(< =>5-10+x=7\)

\(< =>x=7+10-5=12\)

d, \(11+\left(15-x\right)=1\)

\(< =>11+15-x=1\)

\(< =>26-1=25=x\)

Answer 4

e, \(8x-75=5x+21\)

\(< =>8x-5x=21+75=96\)

\(< =>x=\frac{96}{3}=32\)

f, \(9x+25=-\left(2x-58\right)\)

\(< =>9x+25=-2x+58\)

\(< =>9x+2x=58-25=33\)

\(< =>x=\frac{33}{11}=3\)

g, \(|x+3|=4< =>\orbr{\begin{cases}x+3=4\\x+3=-4\end{cases}}\)

\(< =>\orbr{\begin{cases}x=1\\x=-7\end{cases}}\)

h, \(15-|2x-1|=|-8|\)

\(< =>15-|2x-1|=8\)

\(< =>|2x-1|=7< =>\orbr{\begin{cases}2x-1=7\\2x-1=-7\end{cases}}\)

\(< =>\orbr{\begin{cases}2x=8\\2x=-6\end{cases}< =>\orbr{\begin{cases}x=4\\x=-3\end{cases}}}\)