Studdy AI Logo
Math

QuestionSolve the inequality 4∣t+3∣≥84|t+3| \geq 8 and express the solution in interval notation using decimals.

Studdy Solution

STEP 1

Assumptions1. We are given the absolute value inequality 4∣t+3∣≥84|t+3| \geq8. . We need to solve this inequality and express the answer in interval notation.

STEP 2

First, we can simplify the inequality by dividing both sides by4.
∣t+∣≥2|t+| \geq2

STEP 3

The absolute value inequality ∣t+3∣≥2|t+3| \geq2 can be rewritten as two separate inequalities t+3≥2t+3 \geq2 and t+3≤−2t+3 \leq -2.

STEP 4

Now, we solve the first inequality t+3≥2t+3 \geq2 by subtracting3 from both sides.
t≥2−3t \geq2 -3

STEP 5

Calculate the value of t.
t≥−1t \geq -1

STEP 6

Next, we solve the second inequality t+3≤−2t+3 \leq -2 by subtracting3 from both sides.
t≤−2−3t \leq -2 -3

STEP 7

Calculate the value of t.
t≤−5t \leq -5

STEP 8

The solution to the inequality 4∣t+3∣≥84|t+3| \geq8 is the union of the solutions to the two inequalities t≥−1t \geq -1 and t≤−5t \leq -5. In interval notation, this is expressed as (−∞,−5]∪[−1,∞)(-\infty, -5] \cup [-1, \infty).
The solution to the inequality is (−∞,−5]∪[−1,∞)(-\infty, -5] \cup [-1, \infty).

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