Math

QuestionSolve the equation 3y+6=13|3y + 6| = 13 and select the solution set: A. List answers or B. \varnothing.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is always non-negative. . The equation is in the form of |ax + b| = c, where a, b, and c are constants.
3. The solution set could be empty if there are no real solutions.

STEP 2

First, we need to understand that the absolute value of a number is its distance from zero on the number line. Therefore, it can be either positive or negative. This gives us two equations to solvey+6=13y +6 =13andy+6=13y +6 = -13

STEP 3

Let's solve the first equation. Start by subtracting6 from both sides.
3y=1363y =13 -6

STEP 4

implify the right side of the equation.
3y=73y =7

STEP 5

Next, divide both sides by3 to solve for y.
y=7/3y =7 /3

STEP 6

Calculate the value of y.
y=/3=2.33y = /3 =2.33

STEP 7

Now, let's solve the second equation. Start by subtracting6 from both sides.
3y=1363y = -13 -6

STEP 8

implify the right side of the equation.
3y=193y = -19

STEP 9

Next, divide both sides by3 to solve for y.
y=19/3y = -19 /3

STEP 10

Calculate the value of y.
y=19/3=6.33y = -19 /3 = -6.33The solution set is {2.33, -6.33}.

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