What values of x satisfy |x - 4| + |x + 4| <= 10$?

Express your answer in interval notation.

ive found out the answers of [4,5] or [-5,-4]

and dont understand where i went wrong in the problem.

Can someone explain?

Guest Aug 28, 2018

#1**+2 **

|x - 4| + |x + 4| <= 10

We have these equations

x - 4 + x + 4 <= 10

2x <= 10

x <= 5

And

x - 4 + x + 4 >= -10

2x >= -10

x >= -5

So.....the solution is [-5 , 5 ]

Here's the graph of the solution : https://www.desmos.com/calculator/7ar4jqmtg3

CPhill Aug 28, 2018

#2**+3 **

**What values of x satisfy |x - 4| + |x + 4| <= 10 ?**

**Express your answer in interval notation.**

**\( \huge |x + 4| + |x - 4| \le 10\)**

Here we have two different amounts.

To dissolve them, we must make a double case distinction.

Usually we did this one after the other.

For reasons of space, we start with the first case in which the content of the left amount

is greater than or equal to zero.

\(\begin{array}{|rcll|} \hline & \underline{x\ge -4:}& \\\\ & x+4 + |x-4 | \le 10 \\ \\ \underline{\text{for } x\ge 4:} && \underline{\text{for } x \lt 4: } \\\\ x+4+x-4 \le 10 && x+4-(x-4) \le 10 \\ 2x \le 10 && 8 \le 10 \\ \boxed{ x \le 5 } && \\ \hline \end{array} \)

The other case was \(x \lt -4\).

In this area the content of the right amount is

always negative. A further case distinction is therefore not necessary here.

\(\begin{array}{|rcll|} \hline & \underline{x \lt -4:} \\\\ & -(x+4) - (x-4) \le 10 \\ \\ & -x-4-x+4 \le 10 \\ & -2x \le 10 \quad & \quad :(-2)\\ & x \ge \dfrac{10}{-2} \\ & \boxed{x \ge -5} \\ \hline \end{array} \)

Values of **x** in interval notation:** [-5 , 5 ]**

heureka Aug 29, 2018