在维基据一种href="//www.parkandroid.com/wiki/representation-on-the-real-line/" class="wiki_link" title="实线上的表示“target="_blank">实线上的表示据/a>,我们看到实数可以直观地表示在一条数轴上,直线上的每个点对应一个实数,每个实数对应直线上的一个点。我们怎样用数轴来表示实数的集合呢?据/p>
当我们绘制数字线的区域时,我们使用以下约定:据/p>
- 实点和彩色线表示区域中包含的点。据/li>
- 开放(未填充的)点不包含在该区域分别表示点。据/li>
让我们看一个例子。据/p>
在数轴上找一个表示上述区域的不等式。据/p>
因为圆上有实数据span class="katex">
−据/span>3.据/span>是一个开放的圆圈,据span class="katex">
−据/span>3.据/span>不包括在该地区。这表明该区域包含严格大于的所有实数据span class="katex">
−据/span>3.据/span>,即所有实数据span class="katex">
X据/span>满足上据span class="katex">
X据/span>>据/span>−据/span>3.据/span>.据span class="katex">
□据/span>
现在,我们将考虑数轴上的同一区域,并证明可能有多个不等式来代表同一区域。据/p>
下面哪个不等式在上面的数轴上表示?据/p>
(据/span>一种据/span>)据/span>X据/span>+据/span>8.据/span>≤据/span>2据/span>X据/span>(据/span>B.据/span>)据/span>2据/span>X据/span>−据/span>3.据/span>>据/span>X据/span>+据/span>4.据/span>(据/span>C据/span>)据/span>−据/span>X据/span>+据/span>3.据/span>据据/span>4.据/span>X据/span>+据/span>1据/span>8.据/span>(据/span>D.据/span>)据/span>3.据/span>X据/span>+据/span>9.据/span>≤据/span>−据/span>2据/span>X据/span>−据/span>1据/span>
以上不等式的解是据/p>
(据/span>B.据/span>)据/span>2据/span>X据/span>−据/span>3.据/span>>据/span>X据/span>+据/span>4.据/span>(据/span>C据/span>)据/span>−据/span>X据/span>+据/span>3.据/span>据据/span>4.据/span>X据/span>+据/span>1据/span>8.据/span>(据/span>D.据/span>)据/span>3.据/span>X据/span>+据/span>9.据/span>≤据/span>−据/span>2据/span>X据/span>−据/span>1据/span>(据/span>一种据/span>)据/span>X据/span>+据/span>8.据/span>≤据/span>2据/span>X据/span>⟹据/span>X据/span>>据/span>7.据/span>⟹据/span>X据/span>>据/span>−据/span>3.据/span>⟹据/span>X据/span>≤据/span>−据/span>2据/span>.据/span>⟹据/span>X据/span>≥据/span>8.据/span>
因此,答案是据span class="katex">
(据/span>C据/span>)据/span>.据/span>
□据/span>
这个例子表明,在能够确定不等式是否代表数字行中的给定区域之前,可能需要对不等式执行代数运算。可能的代数操作包括据/p>
- 加或减一个恒定的两侧;据/li>
- 两边乘以一个正数;据/li>
- 两边同时乘以一个负数,并交换不等号。据/li>
下列哪行数代表的不平等据/p>
2据/span>X据/span>−据/span>1据/span>1据/span>≤据/span>−据/span>(据/span>X据/span>+据/span>2据/span>)据/span>还是据/span>
我们有据/p>
2据/span>X据/span>−据/span>1据/span>1据/span>2据/span>X据/span>−据/span>1据/span>1据/span>3.据/span>X据/span>X据/span>≤据/span>−据/span>(据/span>X据/span>+据/span>2据/span>)据/span>≤据/span>−据/span>X据/span>−据/span>2据/span>≤据/span>9.据/span>≤据/span>3.据/span>.据/span>
因此,答案是据span class="katex">
(据/span>B.据/span>)据/span>.据/span>
□据/span>
下面哪个不等式在上面的数轴上表示?据/p>
(据/span>一种据/span>)据/span>1据/span>0.据/span>0.据/span>X据/span>据据/span>5.据/span>X据/span>+据/span>5.据/span>0.据/span>1据/span>9.据/span>(据/span>B.据/span>)据/span>5.据/span>1据/span>−据/span>5.据/span>2据/span>X据/span>>据/span>5.据/span>X据/span>−据/span>1据/span>(据/span>C据/span>)据/span>2据/span>X据/span>−据/span>1据/span>据据/span>4.据/span>X据/span>+据/span>3.据/span>(据/span>D.据/span>)据/span>4.据/span>3.据/span>X据/span>+据/span>1据/span>据据/span>3.据/span>X据/span>−据/span>1据/span>
以上不等式的解是据/p>
(据/span>B.据/span>)据/span>5.据/span>1据/span>−据/span>5.据/span>2据/span>X据/span>>据/span>5.据/span>X据/span>−据/span>1据/span>(据/span>C据/span>)据/span>2据/span>X据/span>−据/span>1据/span>据据/span>4.据/span>X据/span>+据/span>3.据/span>(据/span>D.据/span>)据/span>4.据/span>3.据/span>X据/span>+据/span>1据/span>据据/span>3.据/span>X据/span>−据/span>1据/span>(据/span>一种据/span>)据/span>1据/span>0.据/span>0.据/span>X据/span>据据/span>5.据/span>X据/span>+据/span>5.据/span>0.据/span>1据/span>9.据/span>⟹据/span>5.据/span>3.据/span>X据/span>据据/span>5.据/span>6.据/span>⟹据/span>4.据/span>2据/span>X据/span>−据/span>2据/span>据据/span>4.据/span>X据/span>+据/span>3.据/span>⟹据/span>1据/span>2据/span>9.据/span>X据/span>+据/span>3.据/span>据据/span>1据/span>2据/span>4.据/span>X据/span>−据/span>1据/span>2据/span>⟹据/span>1据/span>0.据/span>0.据/span>1据/span>9.据/span>X据/span>>据/span>−据/span>1据/span>0.据/span>0.据/span>3.据/span>8.据/span>⟹据/span>X据/span>据据/span>2据/span>⟹据/span>X据/span>据据/span>5.据/span>⟹据/span>X据/span>据据/span>−据/span>3.据/span>.据/span>⟹据/span>X据/span>>据/span>−据/span>2据/span>
因此,答案是据span class="katex">
(据/span>C据/span>)据/span>.据/span>
□据/span>
以上哪条数轴表示下列线性不等式系统的解?据/p>
{据/span>2据/span>X据/span>−据/span>1据/span>X据/span>+据/span>1据/span>≤据/span>>据/span>X据/span>+据/span>5.据/span>0.据/span>
第一个不等式给出据span class="katex">
X据/span>≤据/span>6.据/span>.据/span>第二个不等式给出据span class="katex">
X据/span>>据/span>−据/span>1据/span>.据/span>因此,解决方案是据span class="katex">
−据/span>1据/span>据据/span>X据/span>≤据/span>6.据/span>那据/span>这意味着数行的适当的代表是据span class="katex">
(据/span>一种据/span>)据/span>.据/span>
□据/span>