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galina1969 [7]
4 years ago
10

Which of the following is a solution to...Please answer asap

Mathematics
2 answers:
MrRa [10]4 years ago
8 0

Answer:

C. x\le -5 \text{ or }\ x\ge -1

Step-by-step explanation:

Consider inequality 4|x+3|\ge 8

Divide it by 4:

|x+3|\ge 2

This inequality is equivalent to two inequalities:

\left\[\begin{array}{l}x+3\ge 2\\x+3\le -2\end{array}\right.

Hence

\left\[\begin{array}{l}x\ge -1\\x\le -5\end{array}\right.

So,

x\le -5 \text{ or }\ x\ge -1

torisob [31]4 years ago
3 0

Start with

4|x+3|\geq 8

Divide both sides by 4:

|x+3|\geq 2

Now we "solve" the absolute value. It depends on the sign of its argument, so we have:

CASE 1: x+3>0

In this case, i.e. if x>-3, the argument of the absolute value is positive, and so it remains unchanged. The equation becomes

x+3\geq 2 \iff x \geq -1

We can accept this solution, because it is compatible with the request x>-3.

CASE 2: x+3<0

In this case, i.e. if x<-3, the argument of the absolute value is negative, and so its sign is inverted. The equation becomes

-x-3\geq 2 \iff -x \geq 5 \iff x \leq -5

We can accept this solution, because it is compatible with the request x<-3.

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