Tìm x
a, | 1$\frac{2}{3}$ -2x| <5
b, | 3-5x|>8
c, | $\frac{3}{4}$ -2x|+x <13
d, | -3$\frac{3}{4}$ -3x| -2x>15
Tìm x a, | 1$\frac{2}{3}$ -2x| <5 b, | 3-5x|>8 c, | $\frac{3}{4}$ -2x|+x <13 d, | -3$\frac{3}{4}$ -3x| -2x>15
By Raelynn
By Raelynn
Tìm x
a, | 1$\frac{2}{3}$ -2x| <5
b, | 3-5x|>8
c, | $\frac{3}{4}$ -2x|+x <13
d, | -3$\frac{3}{4}$ -3x| -2x>15
Đáp án:
d. \(\left[ \begin{array}{l}
x < – \dfrac{{15}}{4}\\
x > \dfrac{{45}}{4}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a.\left| {\dfrac{5}{3} – 2x} \right| < 5\\
\to \left[ \begin{array}{l}
\dfrac{5}{3} – 2x < 5\\
\dfrac{5}{3} – 2x > – 5
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x > – \dfrac{{10}}{3}\\
2x < \dfrac{{20}}{3}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x > – \dfrac{5}{3}\\
x < \dfrac{{10}}{3}
\end{array} \right.\\
b.\left| {3 – 5x} \right| > 8\\
\to \left[ \begin{array}{l}
3 – 5x > 8\\
3 – 5x < – 8
\end{array} \right.\\
\to \left[ \begin{array}{l}
5x < – 5\\
5x > 11
\end{array} \right.\\
\to \left[ \begin{array}{l}
x < – 1\\
x > \dfrac{{11}}{5}
\end{array} \right.\\
c.\left| {\dfrac{3}{4} – 2x} \right| < 13 – x\\
\to \left[ \begin{array}{l}
\dfrac{3}{4} – 2x < 13 – x\\
\dfrac{3}{4} – 2x > – 13 + x
\end{array} \right.\\
\to \left[ \begin{array}{l}
x > – \dfrac{{49}}{4}\\
3x < \dfrac{{55}}{4}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x > – \dfrac{{49}}{4}\\
x < \dfrac{{55}}{{12}}
\end{array} \right.\\
d.\left| { – \dfrac{{15}}{4} – 3x} \right| > 15 + 2x\\
\to \left[ \begin{array}{l}
– \dfrac{{15}}{4} – 3x > 15 + 2x\\
– \dfrac{{15}}{4} – 3x < – 15 – 2x
\end{array} \right.\\
\to \left[ \begin{array}{l}
5x < – \dfrac{{75}}{4}\\
x > \dfrac{{45}}{4}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x < – \dfrac{{15}}{4}\\
x > \dfrac{{45}}{4}
\end{array} \right.
\end{array}\)