2025年不等式組題目及答案一、單項(xiàng)選擇題1.不等式組\(\begin{cases}x+3>5\\2x-1<7\end{cases}\)的解集是？A.\(x>2\)B.\(x<4\)C.\(2<x<4\)D.\(x<2\)或\(x>4\)答案：C2.不等式組\(\begin{cases}3x-2\leq7\\x+4>6\end{cases}\)的解集是？A.\(x\leq3\)B.\(x>2\)C.\(2<x\leq3\)D.\(x<2\)或\(x\geq3\)答案：C3.不等式組\(\begin{cases}x^2-4\leq0\\x+1>0\end{cases}\)的解集是？A.\(-1<x\leq2\)B.\(-2\leqx\leq2\)C.\(x\leq-1\)或\(x\geq2\)D.\(-1<x<2\)答案：B4.不等式組\(\begin{cases}|x|<3\\x-1>0\end{cases}\)的解集是？A.\(1<x<3\)B.\(-3<x<3\)C.\(x>1\)且\(-3<x<3\)D.\(x<-3\)或\(x>3\)答案：C5.不等式組\(\begin{cases}x^2-9\geq0\\x-3<0\end{cases}\)的解集是？A.\(x\leq-3\)或\(x\geq3\)B.\(-3\leqx\leq3\)C.\(x<3\)D.\(x\leq-3\)或\(3<x\leq9\)答案：C6.不等式組\(\begin{cases}2x+1\geq5\\x-2<0\end{cases}\)的解集是？A.\(x\geq2\)B.\(x<2\)C.\(2\leqx<3\)D.\(x<2\)或\(x\geq3\)答案：C7.不等式組\(\begin{cases}x^2+1\leq2x\\x+1>0\end{cases}\)的解集是？A.\(x<1\)B.\(x=1\)C.\(0<x<1\)D.\(x<-1\)或\(x>1\)答案：C8.不等式組\(\begin{cases}3x-4>2\\x+1\leq4\end{cases}\)的解集是？A.\(x>2\)B.\(x\leq3\)C.\(2<x\leq3\)D.\(x<2\)或\(x>3\)答案：C9.不等式組\(\begin{cases}|x-1|<2\\x+3>0\end{cases}\)的解集是？A.\(-1<x<3\)B.\(-3<x<3\)C.\(x>-1\)且\(-3<x<3\)D.\(x<-3\)或\(x>3\)答案：B10.不等式組\(\begin{cases}x^2-4x+3\leq0\\x-1<0\end{cases}\)的解集是？A.\(1\leqx\leq3\)B.\(x<1\)C.\(x\leq1\)或\(x\geq3\)D.\(1<x<3\)答案：B二、多項(xiàng)選擇題1.不等式組\(\begin{cases}x+2>5\\2x-1<7\end{cases}\)的解集是？A.\(x>3\)B.\(x<4\)C.\(3<x<4\)D.\(x<3\)或\(x>4\)答案：A,B,C2.不等式組\(\begin{cases}3x-2\leq7\\x+4>6\end{cases}\)的解集是？A.\(x\leq3\)B.\(x>2\)C.\(2<x\leq3\)D.\(x<2\)或\(x\geq3\)答案：B,C3.不等式組\(\begin{cases}x^2-4\leq0\\x+1>0\end{cases}\)的解集是？A.\(-1<x\leq2\)B.\(-2\leqx\leq2\)C.\(x\leq-1\)或\(x\geq2\)D.\(-1<x<2\)答案：B4.不等式組\(\begin{cases}|x|<3\\x-1>0\end{cases}\)的解集是？A.\(1<x<3\)B.\(-3<x<3\)C.\(x>1\)且\(-3<x<3\)D.\(x<-3\)或\(x>3\)答案：C5.不等式組\(\begin{cases}x^2-9\geq0\\x-3<0\end{cases}\)的解集是？A.\(x\leq-3\)或\(x\geq3\)B.\(-3\leqx\leq3\)C.\(x<3\)D.\(x\leq-3\)或\(3<x\leq9\)答案：C6.不等式組\(\begin{cases}2x+1\geq5\\x-2<0\end{cases}\)的解集是？A.\(x\geq2\)B.\(x<2\)C.\(2\leqx<3\)D.\(x<2\)或\(x\geq3\)答案：C7.不等式組\(\begin{cases}x^2+1\leq2x\\x+1>0\end{cases}\)的解集是？A.\(x<1\)B.\(x=1\)C.\(0<x<1\)D.\(x<-1\)或\(x>1\)答案：C8.不等式組\(\begin{cases}3x-4>2\\x+1\leq4\end{cases}\)的解集是？A.\(x>2\)B.\(x\leq3\)C.\(2<x\leq3\)D.\(x<2\)或\(x>3\)答案：C9.不等式組\(\begin{cases}|x-1|<2\\x+3>0\end{cases}\)的解集是？A.\(-1<x<3\)B.\(-3<x<3\)C.\(x>-1\)且\(-3<x<3\)D.\(x<-3\)或\(x>3\)答案：B10.不等式組\(\begin{cases}x^2-4x+3\leq0\\x-1<0\end{cases}\)的解集是？A.\(1\leqx\leq3\)B.\(x<1\)C.\(x\leq1\)或\(x\geq3\)D.\(1<x<3\)答案：B三、判斷題1.不等式組\(\begin{cases}x+3>5\\2x-1<7\end{cases}\)的解集是\(x>2\)。答案：錯(cuò)誤2.不等式組\(\begin{cases}3x-2\leq7\\x+4>6\end{cases}\)的解集是\(2<x\leq3\)。答案：正確3.不等式組\(\begin{cases}x^2-4\leq0\\x+1>0\end{cases}\)的解集是\(-1<x\leq2\)。答案：錯(cuò)誤4.不等式組\(\begin{cases}|x|<3\\x-1>0\end{cases}\)的解集是\(1<x<3\)。答案：錯(cuò)誤5.不等式組\(\begin{cases}x^2-9\geq0\\x-3<0\end{cases}\)的解集是\(x<3\)。答案：正確6.不等式組\(\begin{cases}2x+1\geq5\\x-2<0\end{cases}\)的解集是\(2\leqx<3\)。答案：正確7.不等式組\(\begin{cases}x^2+1\leq2x\\x+1>0\end{cases}\)的解集是\(0<x<1\)。答案：正確8.不等式組\(\begin{cases}3x-4>2\\x+1\leq4\end{cases}\)的解集是\(2<x\leq3\)。答案：正確9.不等式組\(\begin{cases}|x-1|<2\\x+3>0\end{cases}\)的解集是\(-3<x<3\)。答案：正確10.不等式組\(\begin{cases}x^2-4x+3\leq0\\x-1<0\end{cases}\)的解集是\(x<1\)。答案：正確四、簡答題1.解不等式組\(\begin{cases}2x-1>3\\x+2<5\end{cases}\)。答案：解第一個(gè)不等式\(2x-1>3\)，得\(x>2\)。解第二個(gè)不等式\(x+2<5\)，得\(x<3\)。因此，不等式組的解集是\(2<x<3\)。2.解不等式組\(\begin{cases}x^2-4\leq0\\x+1>0\end{cases}\)。答案：解第一個(gè)不等式\(x^2-4\leq0\)，得\(-2\leqx\leq2\)。解第二個(gè)不等式\(x+1>0\)，得\(x>-1\)。因此，不等式組的解集是\(-1<x\leq2\)。3.解不等式組\(\begin{cases}|x-1|<2\\x-3<0\end{cases}\)。答案：解第一個(gè)不等式\(|x-1|<2\)，得\(-1<x-1<2\)，即\(0<x<3\)。解第二個(gè)不等式\(x-3<0\)，得\(x<3\)。因此，不等式組的解集是\(0<x<3\)。4.解不等式組\(\begin{cases}3x-4\geq2\\x+1\leq4\end{cases}\)。答案：解第一個(gè)不等式\(3x-4\geq2\)，得\(x\geq2\)。解第二個(gè)不等式\(x+1\leq4\)，得\(x\leq3\)。因此，不等式組的解集是\(2\leqx\leq3\)。五、討論題1.討論不等式組\(\begin{cases}x^2-9\geq0\\x-3<0\end{cases}\)的解集。答案：解第一個(gè)不等式\(x^2-9\geq0\)，得\(x\leq-3\)或\(x\geq3\)。解第二個(gè)不等式\(x-3<0\)，得\(x<3\)。因此，不等式組的解集是\(x\leq-3\)。2.討論不等式組\(\begin{cases}|x|<3\\x-1>0\end{cases}\)的解集。答案：解第一個(gè)不等式\(|x|<3\)，得\(-3<x<3\)。解第二個(gè)不等式\(x-1>0\)，得\(x>1\)。因此，不等式組的解集是\(1<x<3\)。3.討論不等式組\(\begin{cases}2x+1\geq5\\x+1\leq4\end{cases}\)的解集。答案：解第一個(gè)不等式\(2x+1\geq5\)，得\(x\geq2\)。解第二個(gè)不等式\(x+1\leq