Math

Question Solve for the absolute value of uu that satisfies the equation 52u=205|2u| = 20.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 52u=205|2u| = 20.
2. We need to solve for the variable uu.
3. The absolute value function x|x| is defined as xx if x0x \geq 0 and x-x if x<0x < 0.

STEP 2

First, we will isolate the absolute value expression by dividing both sides of the equation by 5.
2u=205|2u| = \frac{20}{5}

STEP 3

Now, perform the division on the right side of the equation.
2u=4|2u| = 4

STEP 4

The equation 2u=4|2u| = 4 means that 2u2u can be either 44 or 4-4 because the absolute value of both 44 and 4-4 is 44.

STEP 5

We will set up two separate equations to solve for uu, one for each case of the absolute value.
Case 1: 2u=42u = 4
Case 2: 2u=42u = -4

STEP 6

Solve for uu in Case 1.
2u=42u = 4

STEP 7

Divide both sides of the equation by 2 to isolate uu in Case 1.
u=42u = \frac{4}{2}

STEP 8

Now, perform the division to find the value of uu in Case 1.
u=2u = 2

STEP 9

Solve for uu in Case 2.
2u=42u = -4

STEP 10

Divide both sides of the equation by 2 to isolate uu in Case 2.
u=42u = \frac{-4}{2}

STEP 11

Now, perform the division to find the value of uu in Case 2.
u=2u = -2
The solutions for uu are u=2u = 2 and u=2u = -2.

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