Solved on Dec 15, 2023

Solve for the absolute value of $u$ that satisfies the equation $5|2u| = 20$ .

STEP 1

Assumptions
1. We are given the equation $5|2u| = 20$ .
2. We need to solve for the variable $u$ .
3. The absolute value function $|x|$ is defined as $x$ if $x \geq 0$ and $-x$ if $x < 0$ .

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

Solve for $u$ in Case 1.
$2u = 4$

STEP 7

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

STEP 8

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

STEP 9

Solve for $u$ in Case 2.
$2u = -4$

STEP 10

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

STEP 11

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

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Solve for the absolute value of $u$ that satisfies the equation $5|2u| = 20$ .

STEP 1

Assumptions
1. We are given the equation $5|2u| = 20$ .
2. We need to solve for the variable $u$ .
3. The absolute value function $|x|$ is defined as $x$ if $x \geq 0$ and $-x$ if $x < 0$ .

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

Solve for $u$ in Case 1.
$2u = 4$

STEP 7

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

STEP 8

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

STEP 9

Solve for $u$ in Case 2.
$2u = -4$

STEP 10

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

STEP 11

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

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Solve for the absolute value of uuu that satisfies the equation 5∣2u∣=205|2u| = 205∣2u∣=20.

STEP 1

Assumptions1. We are given the equation 5∣2u∣=205|2u| = 205∣2u∣=20.2. We need to solve for the variable uuu.3. The absolute value function ∣x∣|x|∣x∣ is defined as xxx if x≥0x \geq 0x≥0 and −x-x−x if x<0x < 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}∣2u∣=520​

STEP 3

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

STEP 4

The equation ∣2u∣=4|2u| = 4∣2u∣=4 means that 2u2u2u can be either 444 or −4-4−4 because the absolute value of both 444 and −4-4−4 is 444.

STEP 5

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

STEP 6

Solve for uuu in Case 1.2u=42u = 42u=4

STEP 7

Divide both sides of the equation by 2 to isolate uuu in Case 1.u=42u = \frac{4}{2}u=24​

STEP 8

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

STEP 9

Solve for uuu in Case 2.2u=−42u = -42u=−4

STEP 10

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

STEP 11

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

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Solve for the absolute value of $u$ that satisfies the equation $5|2u| = 20$ .

Assumptions
1. We are given the equation $5|2u| = 20$ .
2. We need to solve for the variable $u$ .
3. The absolute value function $|x|$ is defined as $x$ if $x \geq 0$ and $-x$ if $x < 0$ .

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

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

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

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

Solve for $u$ in Case 1.
$2u = 4$

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

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

Solve for $u$ in Case 2.
$2u = -4$

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

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