Three-part inequalities on a number line

For an expression like

$-1<=x<5$

Split this into two i.e.

$-1<=x$

And

$x<5$

$-1<=x$ this reads as $-1$ is less than or equal to $x$

$x<5$ this reads $x$ is less than $5$

These can be shown on a number line as

Numbers in the sum show the beginning and end of the inequalities range

Or as:

You can draw it without the arrow too

i.e. without an arrow.

Example 1

Write down the inequality shown in the diagram below:

In this example -5 and 5 are the 2 subjects in the sum including x so -5 and 5 make the range along the number line

Because $x$ is the line between the two circles this can be read as:

The ring above $-5$ shows that $-5$ is less than $x$

$(-5<\x)$

The ring above $+5$ shows that $x$ is less than $5$

$(x<\5)$

Joining the two together

$-5<\x<5$

Answer:

$-5<\x<5$

Example 2

Write down the inequality shown in the diagram below:

in this example -4 is not less than x but is also less than 3

Because $x$ is the line between the two inequalities this can be read as

The ring above $-4$ shows that $-4$ is less than $x$

$(-4<\x)$

The circle above the $3$ shows that $x$ is less than or equal to $3$

$(x<=3)$

Joining the two together

$-4<\x<=3$

Answer:

$-4<\x<=3$