Math

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

Studdy Solution

STEP 1

Assumptions
1. We have an absolute value equation 7y=14|7y| = 14.
2. We need to solve for yy.
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, then x=ax = a or x=ax = -a, where a0a \geq 0.

STEP 3

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

STEP 4

Since the absolute value is equal to 14, we have two scenarios to consider:
1. 7y=147y = 14
2. 7y=147y = -14

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

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

STEP 9

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

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