Solved on Dec 14, 2023

Solve for $y$ where $|7y| = 14$ . Write the solution as an integer or simplified fraction.

STEP 1

Assumptions
1. We have an absolute value equation $|7y| = 14$ .
2. We need to solve for $y$ .
3. We will consider both the positive and negative scenarios that satisfy the absolute value.

STEP 2

The definition of absolute value states that if $|x| = a$ , then $x = a$ or $x = -a$ , where $a \geq 0$ .

STEP 3

Apply the definition of absolute value to the given equation $|7y| = 14$ .

STEP 4

Since the absolute value is equal to 14, we have two scenarios to consider:
1. $7y = 14$
2. $7y = -14$

STEP 5

First, solve for $y$ in the equation $7y = 14$ .
$y = \frac{14}{7}$

STEP 6

Calculate the value of $y$ for the first scenario.
$y = \frac{14}{7} = 2$

STEP 7

Now, solve for $y$ in the equation $7y = -14$ .
$y = \frac{-14}{7}$

STEP 8

Calculate the value of $y$ for the second scenario.
$y = \frac{-14}{7} = -2$

STEP 9

Combine the results from both scenarios to provide the full solution for $y$ .
The solution for $y$ is:
$y = 2 \text{ or } y = -2$

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Solve for $y$ where $|7y| = 14$ . Write the solution as an integer or simplified fraction.

STEP 1

Assumptions
1. We have an absolute value equation $|7y| = 14$ .
2. We need to solve for $y$ .
3. We will consider both the positive and negative scenarios that satisfy the absolute value.

STEP 2

The definition of absolute value states that if $|x| = a$ , then $x = a$ or $x = -a$ , where $a \geq 0$ .

STEP 3

Apply the definition of absolute value to the given equation $|7y| = 14$ .

STEP 4

Since the absolute value is equal to 14, we have two scenarios to consider:
1. $7y = 14$
2. $7y = -14$

STEP 5

First, solve for $y$ in the equation $7y = 14$ .
$y = \frac{14}{7}$

STEP 6

Calculate the value of $y$ for the first scenario.
$y = \frac{14}{7} = 2$

STEP 7

Now, solve for $y$ in the equation $7y = -14$ .
$y = \frac{-14}{7}$

STEP 8

Calculate the value of $y$ for the second scenario.
$y = \frac{-14}{7} = -2$

STEP 9

Combine the results from both scenarios to provide the full solution for $y$ .
The solution for $y$ is:
$y = 2 \text{ or } y = -2$

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Solve for yyy where ∣7y∣=14|7y| = 14∣7y∣=14. Write the solution as an integer or simplified fraction.

STEP 1

Assumptions1. We have an absolute value equation ∣7y∣=14|7y| = 14∣7y∣=14.2. We need to solve for yyy.3. We will consider both the positive and negative scenarios that satisfy the absolute value.

STEP 2

The definition of absolute value states that if ∣x∣=a|x| = a∣x∣=a, then x=ax = ax=a or x=−ax = -ax=−a, where a≥0a \geq 0a≥0.

STEP 3

Apply the definition of absolute value to the given equation ∣7y∣=14|7y| = 14∣7y∣=14.

STEP 4

Since the absolute value is equal to 14, we have two scenarios to consider:1. 7y=147y = 147y=142. 7y=−147y = -147y=−14

STEP 5

First, solve for yyy in the equation 7y=147y = 147y=14.y=147y = \frac{14}{7}y=714​

STEP 6

Calculate the value of yyy for the first scenario.y=147=2y = \frac{14}{7} = 2y=714​=2

STEP 7

Now, solve for yyy in the equation 7y=−147y = -147y=−14.y=−147y = \frac{-14}{7}y=7−14​

STEP 8

Calculate the value of yyy for the second scenario.y=−147=−2y = \frac{-14}{7} = -2y=7−14​=−2

STEP 9

Combine the results from both scenarios to provide the full solution for yyy.The solution for yyy is:y=2 or y=−2y = 2 \text{ or } y = -2y=2 or y=−2

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve for $y$ where $|7y| = 14$ . Write the solution as an integer or simplified fraction.

Assumptions
1. We have an absolute value equation $|7y| = 14$ .
2. We need to solve for $y$ .
3. We will consider both the positive and negative scenarios that satisfy the absolute value.

The definition of absolute value states that if $|x| = a$ , then $x = a$ or $x = -a$ , where $a \geq 0$ .

Apply the definition of absolute value to the given equation $|7y| = 14$ .

Since the absolute value is equal to 14, we have two scenarios to consider:
1. $7y = 14$
2. $7y = -14$

First, solve for $y$ in the equation $7y = 14$ .
$y = \frac{14}{7}$

Calculate the value of $y$ for the first scenario.
$y = \frac{14}{7} = 2$

Now, solve for $y$ in the equation $7y = -14$ .
$y = \frac{-14}{7}$

Calculate the value of $y$ for the second scenario.
$y = \frac{-14}{7} = -2$

Combine the results from both scenarios to provide the full solution for $y$ .
The solution for $y$ is:
$y = 2 \text{ or } y = -2$