Bài 25 trang 16 SGK Toán 7 tập 1

Đề bài

 Tìm \(x\), biết:

a) \(|x -1,7| = 2,3\)  

b) \(\left| {x + \dfrac{3}{4}} \right| - \dfrac{1}{3} = 0\)

Lời giải

a) \( |x -1,7| = 2,3\)

\(\eqalign{
& \Rightarrow \left[ \matrix{
x - 1,7 = 2,3 \hfill \cr
x - 1,7 = - 2,3 \hfill \cr} \right. \cr
& \Rightarrow \left[ \matrix{
x = 2,3 + 1,7 \hfill \cr
x = - 2,3 + 1,7 \hfill \cr} \right. \cr
& \Rightarrow \left[ \matrix{
x = 4 \hfill \cr
x = - 0,6 \hfill \cr} \right. \cr} \)

Vậy \(x = 4\) hoặc \(x = -0,6\)

b)

\(\begin{array}{l}
\left| {x + \dfrac{3}{4}} \right| - \dfrac{1}{3} = 0\\
\left| {x + \dfrac{3}{4}} \right| = \dfrac{1}{3}\\
\text{Trường hợp 1}:\\x + \dfrac{3}{4} = \dfrac{1}{3}\\x = \dfrac{1}{3} - \dfrac{3}{4}\\
x = \dfrac{{ - 5}}{{12}}\\
\text{Trường hợp 2}:\\x + \dfrac{3}{4} =  - \dfrac{1}{3}\\x =  - \dfrac{1}{3} - \dfrac{3}{4}\\
x = \dfrac{{ - 13}}{{12}}
\end{array}\)

Vậy \( x = \dfrac{{ - 5}}{{12}}\) hoặc \({x = \dfrac{{ - 13}}{{12}}}\).


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