Question

I x +1 I =5

I 1/4 -2x I=3/4

Answer 1

\(\left|x-1\right|=5\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=5\left(x>1\right)\\x-1=-5\left(x< 1\right)\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=6\\x=-4\end{cases}}\)

\(\left|\frac{1}{4}-2x\right|=\frac{3}{4}\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{4}-2x=\frac{3}{4}\left(x\le\frac{1}{16}\right)\\\frac{1}{4}-2x=-\frac{3}{4}\left(x>\frac{1}{16}\right)\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{4}\\x=\frac{1}{2}\end{cases}}\)

Answer 2

1. | x+1 |= 5

==> x+1=5 hoặc x+1=—5

==> x=5–1 hoặc x=-5 —1

Nên x= 4 hoặc x= -6

2.| 1/4–2x|= 3/4

==> 1/4–2x= 3/4 hoặc 1/4–2x= —3/4

        2x=1/4–3/4 hoặc 2x=1/4–(—3/4)

       2x= -1/2 hoặc 2x= 1

        x=(—1/2):2 hoặc x= 1:2

       x= -1/4 hoặc x=1/2