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Question Solve for yy where ∣3y+6∣=12|3y+6|=12. Solutions: y=−6,y=2y=-6, y=2.

Studdy Solution

STEP 1

Assumptions
1. We are given the absolute value equation ∣3y+6∣=12|3y + 6| = 12.
2. We need to solve for the variable yy.
3. The absolute value of a number is its distance from zero on the number line, which means it is always non-negative.
4. An absolute value equation ∣x∣=a|x| = a has two possible solutions: x=ax = a and x=−ax = -a if a≥0a \geq 0.

STEP 2

We will split the absolute value equation into two separate linear equations, because the expression inside the absolute value can be either positive or negative.
3y+6=12or3y+6=−123y + 6 = 12 \quad \text{or} \quad 3y + 6 = -12

STEP 3

First, we solve the equation where the expression inside the absolute value is positive:
3y+6=123y + 6 = 12

STEP 4

Subtract 6 from both sides of the equation to isolate the term with the variable yy.
3y=12−63y = 12 - 6

STEP 5

Calculate the right-hand side of the equation.
3y=63y = 6

STEP 6

Divide both sides of the equation by 3 to solve for yy.
y=63y = \frac{6}{3}

STEP 7

Calculate the value of yy.
y=2y = 2

STEP 8

Now, we solve the equation where the expression inside the absolute value is negative:
3y+6=−123y + 6 = -12

STEP 9

Subtract 6 from both sides of the equation to isolate the term with the variable yy.
3y=−12−63y = -12 - 6

STEP 10

Calculate the right-hand side of the equation.
3y=−183y = -18

STEP 11

Divide both sides of the equation by 3 to solve for yy.
y=−183y = \frac{-18}{3}

STEP 12

Calculate the value of yy.
y=−6y = -6
The solutions for the equation ∣3y+6∣=12|3y + 6| = 12 are y=2y = 2 and y=−6y = -6.

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