Toán Lớp 7: tim̀ x, biết:
2|x+2|+|4-x|=11
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Toán Lớp 7: tim̀ x, biết:
2|x+2|+|4-x|=11
Comments ( 1 )
x < – 2 \Rightarrow \left\{ \begin{array}{l}
x + 2 < 0\\
4 – x > 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left| {x + 2} \right| = – \left( {x + 2} \right)\\
\left| {4 – x} \right| = 4 – x
\end{array} \right.\\
2\left| {x + 2} \right| + \left| {4 – x} \right| = 11\\
\Leftrightarrow – 2.\left( {x + 2} \right) + \left( {4 – x} \right) = 11\\
\Leftrightarrow – 2x – 4 + 4 – x = 11\\
\Leftrightarrow – 3x = 11\\
\Leftrightarrow x = – \dfrac{{11}}{3}\,\,\,\,\left( {t/m} \right)
\end{array}\)
– 2 \le x \le 4 \Rightarrow \left\{ \begin{array}{l}
x + 2 \ge 0\\
4 – x \ge 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left| {x + 2} \right| = x + 2\\
\left| {4 – x} \right| = 4 – x
\end{array} \right.\\
2\left| {x + 2} \right| + \left| {4 – x} \right| = 11\\
\Leftrightarrow 2.\left( {x + 2} \right) + \left( {4 – x} \right) = 11\\
\Leftrightarrow 2x + 4 + 4 – x = 11\\
\Leftrightarrow 8 + x = 11\\
\Leftrightarrow x = 3\,\,\,\,\left( {t/m} \right)
\end{array}\)
x > 4 \Rightarrow \left\{ \begin{array}{l}
x + 2 > 0\\
4 – x < 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left| {x + 2} \right| = x + 2\\
\left| {4 – x} \right| = – \left( {4 – x} \right) = x – 4
\end{array} \right.\\
2\left| {x + 2} \right| + \left| {4 – x} \right| = 11\\
\Leftrightarrow 2.\left( {x + 2} \right) + \left( {x – 4} \right) = 11\\
\Leftrightarrow 3x = 11\\
\Leftrightarrow x = \dfrac{{11}}{3}
\end{array}\)