by Tìm x
a) \(\left| {1,5 – 2x} \right| + 0,2 = 2\)
b) \({2^{x – 2}} – {3.2^x} = – 88\)
c) \( (x – 1) : 0,16 = (-9) : (1 – x) \)
d) \(\frac{{25}}{{14}} = \frac{{x + 7}}{{x – 4}}\)
A. a) x = -0,15 hoặc x = 1,65
b) x = 5
\(c)\,x = \frac{{ – 1}}{5}\) hoặc \(x=\frac{{ 11}}{5}\)
d) x = 18
B. a) x = 0,15 hoặc x = 1,65
b) x = 6
\(c)\,x = \frac{{ – 1}}{5}\)
d) x = 10
C. a) x = 0,15 hoặc x = 1,65
b) x = 8
\(c)\,x = \frac{{ – 1}}{6}\)
d) x = 15
D. a) x = 0,15
b) x = 5
\(c)\,x = \frac{{ – 1}}{5}\)
d) x = 18
Hướng dẫn
Chọn đáp án là: A
Phương pháp giải:
+ Bỏ dấu giá trị tuyệt đối
\(\begin{array}{l}a)\,\,\left| {1,5 – 2x} \right| + 0,2 = 2\\\left| {1,5 – 2x} \right| = 1,8\end{array}\)
Suy ra 1,5 – 2x = 1,8 hoặc 1,5 – 2x = -1,8.
+) 1,5 – 2x = 1,8
2x = -0,3
x = – 0,15
+) 1,5 – 2x = -1,8
2x = 3,3
x = 1,65
Vậy x = -0,15 hoặc x = 1,65.
\(\begin{array}{l}b)\,\,\,{2^{x – 2}} – {3.2^x} = – 88\\{2^x}:{2^2} – {3.2^x} = – 88\\{2^x}.\frac{1}{4} – {3.2^x} = – 88\\{2^x}\left( {\frac{1}{4} – 3} \right) = – 88\\{2^x}.\frac{{ – 11}}{4} = – 88\\{2^x} = 32\\\Rightarrow x = 5\end{array}\)
c) \( (x – 1) : 0,16 = (-9) : (1 – x)\)
\(\begin{array}{l}\Leftrightarrow \frac{{x – 1}}{{0,16}} = \frac{9}{{x – 1}}\\ \Leftrightarrow {\left( {x – 1} \right)^2} = 0,16.9\\\Leftrightarrow {\left( {x – 1} \right)^2} = \frac{{36}}{{25}} = {\left( {\frac{6}{5}} \right)^2}\\\Rightarrow x – 1 = \frac{6}{5};x – 1 = \frac{{ – 6}}{5}\\ + )\,\,x – 1 = \frac{6}{5} \Leftrightarrow x = \frac{6}{5} + 1 \Leftrightarrow x = \frac{{11}}{5}\\+ )\,\,x – 1 = \frac{{ – 6}}{5} \Leftrightarrow x = \frac{{ – 6}}{5} + 1 \Leftrightarrow x = \frac{{ – 1}}{5}\end{array}\)
\(\begin{array}{l}d)\,\,\,\frac{{25}}{{14}} = \frac{{x + 7}}{{x – 4}}\\\Leftrightarrow 25.(x – 4) = 14.(x + 7)\\\Leftrightarrow 25x – 100 = 14x + 98\\\Leftrightarrow 11x = 198\\ \Leftrightarrow x = 18\end{array}\)
Chọn A
