Question

graphing inequalities
1.6
graphing inequalities
x < 3
-2 ≤ x < 6
x < -1 or x ≥ 4
writing inequalities
1.9
-4x > 24 1)
2)

Explanation:

Step1: Graph \(x < 3\)

Draw an open - circle at \(x = 3\) on the number line and shade to the left.

Step2: Graph \(-2\leq x<6\)

Draw a closed - circle at \(x=-2\), an open - circle at \(x = 6\) and shade the region between them.

Step3: Graph \(x < - 1\) or \(x\geq4\)

Draw an open - circle at \(x=-1\) and shade to the left, draw a closed - circle at \(x = 4\) and shade to the right.

Step4: Solve \(-4x>24\)

Divide both sides by \(-4\). When dividing an inequality by a negative number, the direction of the inequality sign changes. So \(x<-6\).

Answer:

For \(x < 3\): Open - circle at 3, shade left. For \(-2\leq x<6\): Closed - circle at - 2, open - circle at 6, shade between. For \(x < - 1\) or \(x\geq4\): Open - circle at - 1 shade left, closed - circle at 4 shade right. For \(-4x>24\), \(x < - 6\) (open - circle at - 6, shade left).