Solved on Dec 14, 2023

Find the value of $y$ that satisfies the equation $|y-6|+8=12$ .

STEP 1

Assumptions
1. We are given the equation $|y-6|+8=12$ .
2. We need to solve for the variable $y$ .

STEP 2

First, we need to isolate the absolute value expression on one side of the equation. We can do this by subtracting 8 from both sides of the equation.
$|y-6|+8-8=12-8$

STEP 3

Simplify both sides of the equation.
$|y-6|=4$

STEP 4

The absolute value equation $|y-6|=4$ means that the expression inside the absolute value, $y-6$ , can either be 4 or -4.

STEP 5

Set up two separate equations to solve for $y$ , one for each case of the absolute value.
$y-6=4 \quad \text{or} \quad y-6=-4$

STEP 6

First, solve the equation when $y-6=4$ .
$y-6=4$

STEP 7

Add 6 to both sides of the equation to isolate $y$ .
$y-6+6=4+6$

STEP 8

Simplify the equation to find the first solution for $y$ .
$y=10$

STEP 9

Now, solve the equation when $y-6=-4$ .
$y-6=-4$

STEP 10

Add 6 to both sides of this equation as well to isolate $y$ .
$y-6+6=-4+6$

STEP 11

Simplify the equation to find the second solution for $y$ .
$y=2$

STEP 12

We have found two solutions for the equation $|y-6|+8=12$ .
The solutions are $y=10$ and $y=2$ .

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Find the value of $y$ that satisfies the equation $|y-6|+8=12$ .

STEP 1

Assumptions
1. We are given the equation $|y-6|+8=12$ .
2. We need to solve for the variable $y$ .

STEP 2

First, we need to isolate the absolute value expression on one side of the equation. We can do this by subtracting 8 from both sides of the equation.
$|y-6|+8-8=12-8$

STEP 3

Simplify both sides of the equation.
$|y-6|=4$

STEP 4

The absolute value equation $|y-6|=4$ means that the expression inside the absolute value, $y-6$ , can either be 4 or -4.

STEP 5

Set up two separate equations to solve for $y$ , one for each case of the absolute value.
$y-6=4 \quad \text{or} \quad y-6=-4$

STEP 6

First, solve the equation when $y-6=4$ .
$y-6=4$

STEP 7

Add 6 to both sides of the equation to isolate $y$ .
$y-6+6=4+6$

STEP 8

Simplify the equation to find the first solution for $y$ .
$y=10$

STEP 9

Now, solve the equation when $y-6=-4$ .
$y-6=-4$

STEP 10

Add 6 to both sides of this equation as well to isolate $y$ .
$y-6+6=-4+6$

STEP 11

Simplify the equation to find the second solution for $y$ .
$y=2$

STEP 12

We have found two solutions for the equation $|y-6|+8=12$ .
The solutions are $y=10$ and $y=2$ .

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Find the value of yyy that satisfies the equation ∣y−6∣+8=12|y-6|+8=12∣y−6∣+8=12.

STEP 1

Assumptions1. We are given the equation ∣y−6∣+8=12|y-6|+8=12∣y−6∣+8=12.2. We need to solve for the variable yyy.

STEP 2

First, we need to isolate the absolute value expression on one side of the equation. We can do this by subtracting 8 from both sides of the equation.∣y−6∣+8−8=12−8|y-6|+8-8=12-8∣y−6∣+8−8=12−8

STEP 3

Simplify both sides of the equation.∣y−6∣=4|y-6|=4∣y−6∣=4

STEP 4

The absolute value equation ∣y−6∣=4|y-6|=4∣y−6∣=4 means that the expression inside the absolute value, y−6y-6y−6, can either be 4 or -4.

STEP 5

Set up two separate equations to solve for yyy, one for each case of the absolute value.y−6=4ory−6=−4y-6=4 \quad \text{or} \quad y-6=-4y−6=4ory−6=−4

STEP 6

First, solve the equation when y−6=4y-6=4y−6=4.y−6=4y-6=4y−6=4

STEP 7

Add 6 to both sides of the equation to isolate yyy.y−6+6=4+6y-6+6=4+6y−6+6=4+6

STEP 8

Simplify the equation to find the first solution for yyy.y=10y=10y=10

STEP 9

Now, solve the equation when y−6=−4y-6=-4y−6=−4.y−6=−4y-6=-4y−6=−4

STEP 10

Add 6 to both sides of this equation as well to isolate yyy.y−6+6=−4+6y-6+6=-4+6y−6+6=−4+6

STEP 11

Simplify the equation to find the second solution for yyy.y=2y=2y=2

STEP 12

We have found two solutions for the equation ∣y−6∣+8=12|y-6|+8=12∣y−6∣+8=12.The solutions are y=10y=10y=10 and y=2y=2y=2.

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

Find the value of $y$ that satisfies the equation $|y-6|+8=12$ .

Assumptions
1. We are given the equation $|y-6|+8=12$ .
2. We need to solve for the variable $y$ .

First, we need to isolate the absolute value expression on one side of the equation. We can do this by subtracting 8 from both sides of the equation.
$|y-6|+8-8=12-8$

Simplify both sides of the equation.
$|y-6|=4$

The absolute value equation $|y-6|=4$ means that the expression inside the absolute value, $y-6$ , can either be 4 or -4.

Set up two separate equations to solve for $y$ , one for each case of the absolute value.
$y-6=4 \quad \text{or} \quad y-6=-4$

First, solve the equation when $y-6=4$ .
$y-6=4$

Add 6 to both sides of the equation to isolate $y$ .
$y-6+6=4+6$

Simplify the equation to find the first solution for $y$ .
$y=10$

Now, solve the equation when $y-6=-4$ .
$y-6=-4$

Add 6 to both sides of this equation as well to isolate $y$ .
$y-6+6=-4+6$

Simplify the equation to find the second solution for $y$ .
$y=2$

We have found two solutions for the equation $|y-6|+8=12$ .
The solutions are $y=10$ and $y=2$ .