Math

Question Solve for xx in the equation x6=4\frac{|x|}{6}=4. Write both solutions as equations.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation x6=4\frac{|x|}{6}=4.
2. We need to solve for xx.
3. Since x|x| denotes the absolute value of xx, there can be two possible solutions for xx: one positive and one negative.

STEP 2

First, we need to isolate the absolute value expression by multiplying both sides of the equation by 6.
x=6×4|x| = 6 \times 4

STEP 3

Calculate the result of the multiplication to find the value of x|x|.
x=24|x| = 24

STEP 4

Since the absolute value of xx is 24, there are two possible solutions for xx: x=24x = 24 or x=24x = -24. We can write these as two separate equations.
x=24orx=24x = 24 \quad \text{or} \quad x = -24

STEP 5

We have found both solutions to the equation x6=4\frac{|x|}{6}=4.
The solutions are x=24x = 24 and x=24x = -24.

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