Studdy AI Logo
Math

Question Solve the equation 6−2∣3x+5∣=06-2|3x+5|=0 for xx. The solution(s) are integer(s) or reduced fraction(s).

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 6−2∣3x+5∣=06 - 2|3x + 5| = 0.
2. We need to solve for the variable xx.
3. The absolute value function ∣a∣|a| is defined as aa if a≥0a \geq 0 and −a-a if a<0a < 0.
4. The solutions should be expressed as integers or reduced fractions.

STEP 2

First, we isolate the absolute value term on one side of the equation.
6−2∣3x+5∣=06 - 2|3x + 5| = 0
2∣3x+5∣=62|3x + 5| = 6

STEP 3

Now, divide both sides of the equation by 2 to solve for the absolute value expression.
∣3x+5∣=62|3x + 5| = \frac{6}{2}
∣3x+5∣=3|3x + 5| = 3

STEP 4

The absolute value equation ∣3x+5∣=3|3x + 5| = 3 can be split into two separate equations, since the expression inside the absolute value can be either positive or negative.
3x+5=3or3x+5=−33x + 5 = 3 \quad \text{or} \quad 3x + 5 = -3

STEP 5

First, let's solve the equation where the expression inside the absolute value is positive.
3x+5=33x + 5 = 3

STEP 6

Subtract 5 from both sides of the equation to isolate the term with xx.
3x=3−53x = 3 - 5
3x=−23x = -2

STEP 7

Now, divide both sides by 3 to solve for xx.
x=−23x = \frac{-2}{3}

STEP 8

Next, let's solve the equation where the expression inside the absolute value is negative.
3x+5=−33x + 5 = -3

STEP 9

Subtract 5 from both sides of the equation to isolate the term with xx.
3x=−3−53x = -3 - 5
3x=−83x = -8

STEP 10

Divide both sides by 3 to solve for xx.
x=−83x = \frac{-8}{3}

STEP 11

We have found the two solutions for the equation 6−2∣3x+5∣=06 - 2|3x + 5| = 0.
The solutions are x=−23x = \frac{-2}{3} and x=−83x = \frac{-8}{3}.
Since the problem asks for integers or reduced fractions and our solutions are already in reduced fraction form, we can conclude with the solutions.
x=−23,−83x = \frac{-2}{3}, \frac{-8}{3}

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord