Question

Which compound inequality could be represented by the graph

Answer 1

Answer:

$x\leq 3$  or $x\geq -1$

Step-by-step explanation:

Verify the solution of each case

case 1) we have

$-4\leq x\leq 4$

Divide the compound inequality into two inequalities

$x\leq 4$ ---> solution is the interval (-∞,4]

$-4\leq x$ ---> solution is the interval [-4,∞)

The solution of the compound inequality is

[-4,∞) ∩ (-∞,4] ----> [-4,4]

case 2) we have

$-2\leq x\leq -1$

Divide the compound inequality into two inequalities

$x\leq -1$ ---> solution is the interval (-∞,-1]

$-2\leq x$ ---> solution is the interval [-2,∞)

The solution of the compound inequality is

[-2,∞) ∩ (-∞,-1] ----> [-2,-1]

case 3) we have

$x\leq -1$ ---> solution is the interval (-∞,-1]

or

$x\geq 0$ ---> solution is the interval [0,∞)

The solution of the compound inequality is ----> (-∞,-1]  ∪ [0,∞)

case 4) we have

$x\leq 3$ ---> solution is the interval (-∞,3]        

or

$x\geq -1$ ---> solution is the interval [-1,∞)

The solution of the compound inequality is

(-∞,3]  ∪ [-1,∞) ---->(-∞,∞)