giải bất phương trình:
a) 3x+5 / 2 -1≤ x+2 / 3 +x
b) |x-3″=2x+1
c) |x+3|=|3x+4|
giải bất phương trình: a) 3x+5 / 2 -1≤ x+2 / 3 +x b) |x-3″=2x+1 c) |x+3|=|3x+4|
By Jasmine
By Jasmine
giải bất phương trình:
a) 3x+5 / 2 -1≤ x+2 / 3 +x
b) |x-3″=2x+1
c) |x+3|=|3x+4|
Đáp án:
c) \(x = – \dfrac{1}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{3x + 5}}{2} – 1 \le \dfrac{{x + 2}}{3} + x\\
\to \dfrac{{9x + 15 – 6 – 2x – 4 – 6x}}{6} \le 0\\
\to x + 5 \le 0\\
\to x \le – 5\\
b)\left| {x – 3} \right| = 2x + 1\\
\to \left[ \begin{array}{l}
x – 3 = 2x + 1\left( {DK:x \ge 3} \right)\\
x – 3 = – 2x – 1\left( {DK:x < 3} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = – 4\left( l \right)\\
3x = 2
\end{array} \right.\\
\to x = \dfrac{2}{3}\left( {TM} \right)\\
c)\left| {x + 3} \right| = \left| {3x + 4} \right|\\
\to \left[ \begin{array}{l}
x + 3 = 3x + 4\left( {DK:x \ge – 3} \right)\\
x + 3 = – 3x – 4\left( {DK:x < – 3} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
2x = – 1\\
4x = – 7
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = – \dfrac{1}{2}\left( {TM} \right)\\
x = – \dfrac{7}{4}\left( l \right)
\end{array} \right.
\end{array}\)