Math  /  Algebra

QuestionSolve. If there is more than one solution, separate them with a comma. 8+43x+3=88+4|3 x+3|=-8

Studdy Solution

STEP 1

1. The equation involves an absolute value, which may result in two separate cases to consider.
2. We will isolate the absolute value expression before solving for x x .

STEP 2

1. Isolate the absolute value expression 3x+3 |3x + 3| .
2. Set up two separate equations to solve for x x based on the definition of absolute value.
3. Solve each equation for x x .
4. Check the solutions in the original equation.

STEP 3

First, subtract 8 from both sides of the equation to isolate the term with the absolute value:
8+43x+3=8 8 + 4|3x + 3| = -8 43x+3=88 4|3x + 3| = -8 - 8 43x+3=16 4|3x + 3| = -16

STEP 4

Divide both sides by 4 to further isolate the absolute value:
3x+3=164 |3x + 3| = \frac{-16}{4} 3x+3=4 |3x + 3| = -4

STEP 5

Recognize that an absolute value expression cannot equal a negative number. Therefore, there are no solutions to the equation:
3x+3=4 |3x + 3| = -4
Since the absolute value cannot be negative, the equation has no solutions.

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