QuestionSolve $|2x - 4| \leq 8$ . Choose the correct range for $x$ from the options given.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, and is always non-negative. . The inequality $|x-4| \leq8$ can be split into two separate inequalities $x-4 \leq8$ and $x-4 \geq -8$ .

STEP 2

Let's solve the first inequality $2x-4 \leq8$ .

STEP 3

To isolate $x$ , we first add to both sides of the inequality.
$2x-+ \leq8+$

STEP 4

implify the inequality.
$2x \leq12$

STEP 5

Next, we divide both sides of the inequality by2 to solve for $x$ .
$\frac{2x}{2} \leq \frac{12}{2}$

STEP 6

implify the inequality to find the solution.
$x \leq6$

STEP 7

Now, let's solve the second inequality $2x-4 \geq -$ .

STEP 8

To isolate $x$ , we first add4 to both sides of the inequality.
$2x-4+4 \geq -8+4$

STEP 9

implify the inequality.
$2x \geq -4$

STEP 10

Next, we divide both sides of the inequality by2 to solve for $x$ .
$\frac{2x}{2} \geq \frac{-4}{2}$

STEP 11

implify the inequality to find the solution.
$x \geq -$

STEP 12

The solution to the inequality $|2x-4| \leq8$ is the intersection of the solutions to the two inequalities $2x-4 \leq8$ and $2x-4 \geq -8$ . This means that $x$ must satisfy both inequalities simultaneously.
So, the solution to the inequality is $x \geq -2$ and $x \leq6$ .
The correct option is C. $x \geq -2$ and $x \leq6$ .

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