Represent the following numbers and inequalities on a number line: 1. Numbers: −4, −2, 0, 2, 4. 2…

Question

Represent the following numbers and inequalities on a number line: 1. Numbers: −4, −2, 0, 2, 4. 2. Inequalities: a) −2 <= k <= 1, b) −5 < y <= −2

ScanSolve AI Tutor · Accepted Answer

Here are the representations of the numbers and inequalities on a number line:

1. Represent each of the following numbers on a number line:
Numbers: $-4, -2, 0, 2, 4$

\begin{tikzpicture}
\draw[<->] (-5,0) -- (5,0);
\foreach \x in {-4,-3,-2,-1,0,1,2,3,4}
    \draw (\x,0.1) -- (\x,-0.1) node[below] {$\x$};
\filldraw[black] (-4,0) circle (2pt);
\filldraw[black] (-2,0) circle (2pt);
\filldraw[black] (0,0) circle (2pt);
\filldraw[black] (2,0) circle (2pt);
\filldraw[black] (4,0) circle (2pt);
\end{tikzpicture}

2. Represent each of the following inequalities on a number line:

a) $-2 \le k \le 1$ where $k$ is a real number This means $k$ is greater than or equal to -2 and less than or equal to 1.

\begin{tikzpicture}
\draw[<->] (-4,0) -- (3,0);
\foreach \x in {-3,-2,-1,0,1,2}
    \draw (\x,0.1) -- (\x,-0.1) node[below] {$\x$};
\filldraw[black] (-2,0) circle (2pt);
\filldraw[black] (1,0) circle (2pt);
\draw[line width=1.5pt] (-2,0) -- (1,0);
\end{tikzpicture}

b) $-5 < y \le -2$ where $y$ is a real number This means $y$ is greater than -5 and less than or equal to -2.

\begin{tikzpicture}
\draw[<->] (-6,0) -- (0,0);
\foreach \x in {-5,-4,-3,-2,-1}
    \draw (\x,0.1) -- (\x,-0.1) node[below] {$\x$};
\draw[white, line width=1.5pt] (-5,0) circle (2pt); % White circle for open interval
\draw[black] (-5,0) circle (2pt); % Black outline for open interval
\filldraw[black] (-2,0) circle (2pt);
\draw[line width=1.5pt] (-5,0) -- (-2,0);
\end{tikzpicture}

c) $-2 < x < 4$ where $x$ is a real number This means $x$ is greater than -2 and less than 4.

\begin{tikzpicture}
\draw[<->] (-3,0) -- (5,0);
\foreach \x in {-2,-1,0,1,2,3,4}
    \draw (\x,0.1) -- (\x,-0.1) node[below] {$\x$};
\draw[white, line width=1.5pt] (-2,0) circle (2pt); % White circle for open interval
\draw[black] (-2,0) circle (2pt); % Black outline for open interval
\draw[white, line width=1.5pt] (4,0) circle (2pt); % White circle for open interval
\draw[black] (4,0) circle (2pt); % Black outline for open interval
\draw[line width=1.5pt] (-2,0) -- (4,0);
\end{tikzpicture}

Represent the following numbers and inequalities on a number line: 1. Numbers: -4, -2, 0, 2, 4. 2. Inequalities: a) -2 <= k <= 1, b) −5 < y <= -2

Still stuck on this one?

More Mathematics Questions