Question

for each equation or inequality below, graph the set of all rational numbers which are solutions.
x > 1
x < 2
x ≤ 2
x ≥ - 4
x ≠ - 3
x ≥ 1.5
x < 2 1/3
x ≠ 4.4
x ≤ 0
x ≯ 2
|x| > 3

Explanation:

Step1: Identify inequality type

Determine if it's strict (\(>\) or \(<\)) or non - strict (\(\geq\) or \(\leq\)) or not equal (\(
eq\)).

Step2: Locate boundary point

Mark the value on the number line. Open - circle for strict inequalities, closed - circle for non - strict.

Step3: Shade appropriate region

Shade to the right for \(>\) or \(\geq\), to the left for \(<\) or \(\leq\). For \(
eq\), shade both regions except the point. For absolute - value inequalities, rewrite and follow the above steps.

Answer:

1. For \(x > 1\): Draw an open - circle at \(x = 1\) and shade the number line to the right of \(1\).
2. For \(x<2\): Draw an open - circle at \(x = 2\) and shade the number line to the left of \(2\).
3. For \(x\leq2\): Draw a closed - circle at \(x = 2\) and shade the number line to the left of \(2\).
4. For \(x\geq - 4\): Draw a closed - circle at \(x=-4\) and shade the number line to the right of \(-4\).
5. For \(x

eq - 3\): Draw open - circles at \(x=-3\) and shade the number line except at \(x = - 3\) (shade both the left and right parts of \(-3\)).

1. For \(x\geq1.5\): Draw a closed - circle at \(x = 1.5\) and shade the number line to the right of \(1.5\).
2. For \(x<2\frac{1}{3}\) (or \(x < \frac{7}{3}\approx2.33\)): Draw an open - circle at \(x=\frac{7}{3}\) and shade the number line to the left of \(\frac{7}{3}\).
3. For \(x

eq4.4\): Draw open - circles at \(x = 4.4\) and shade the number line except at \(x = 4.4\) (shade both the left and right parts of \(4.4\)).

1. For \(x\leq0\): Draw a closed - circle at \(x = 0\) and shade the number line to the left of \(0\).
2. For \(x

ot>2\) (or \(x\leq2\)): Draw a closed - circle at \(x = 2\) and shade the number line to the left of \(2\).

1. For \(|x|>3\), which is equivalent to \(x>3\) or \(x < - 3\): Draw open - circles at \(x=-3\) and \(x = 3\), shade the number line to the left of \(-3\) and to the right of \(3\).