QuestionSolve for $x$ : $2|3x+1|-4=6$ . What are the possible values of $x$ ?

Studdy Solution

STEP 1

Assumptions1. The absolute value function is defined as $|x| = x$ for $x \geq0$ and $|x| = -x$ for $x <0$ . . The equation to solve is $|3x+1|-4=6$ .

STEP 2

First, we need to isolate the absolute value function. We can do this by adding4 to both sides of the equation.
$2|x+1| =6 +4$

STEP 3

Now, simplify the right side of the equation.
$2|3x+1| =10$

STEP 4

Next, we need to further isolate the absolute value function. We can do this by dividing both sides of the equation by2.
$|3x+1| = \frac{10}{2}$

STEP 5

implify the right side of the equation.
$|3x+1| =5$

STEP 6

Now, we can split the equation into two cases, one for $3x+1 \geq0$ and one for $3x+1 <0$ .
Case1 $3x+1 \geq0$
$3x+1 =5$ Case2 $3x+1 <0$
$-(3x+1) =5$

STEP 7

Now, solve for $x$ in both cases.
Case1 $3x+1 =5$
$3x =5 -1$ Case2 $-(3x+1) =5$
$-3x -1 =5$

STEP 8

implify both equations.
Case1 $3x =4$
$x = \frac{4}{3}$ Case2 $-3x -1 =5$
$-3x =5 +1$

STEP 9

olve for $x$ in the second case.
$-3x =6$ $x = -\frac{6}{3}$

STEP 10

implify the solution for the second case.
$x = -2$ So, the solutions for the equation $2|3x+|-4=6$ are $x=\frac{4}{3}$ and $x=-2$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms