Math  /  Algebra

Question- Q20: Solve and express in interval notation: 3x+14|3 x+1| \geq 4. - Q21: Solve and express in interval notation: 2x7>3|2 x-7|>3.

Studdy Solution
Combine the solutions from STEP_2 and STEP_3. The solution in interval notation is:
x(,53][1,) x \in (-\infty, -\frac{5}{3}] \cup [1, \infty)
---
## Q21: Solve and express in interval notation: 2x7>3 |2x - 7| > 3 .
STEP_1: Set up the two inequalities:
2x7>3or2x7<3 2x - 7 > 3 \quad \text{or} \quad 2x - 7 < -3
STEP_2: Solve the inequality 2x7>3 2x - 7 > 3 :
2x7>3 2x - 7 > 3 2x>10 2x > 10 x>5 x > 5
STEP_3: Solve the inequality 2x7<3 2x - 7 < -3 :
2x7<3 2x - 7 < -3 2x<4 2x < 4 x<2 x < 2
STEP_4: Combine the solutions from STEP_2 and STEP_3. The solution in interval notation is:
x(,2)(5,) x \in (-\infty, 2) \cup (5, \infty)
The solutions are: - For Q20: x(,53][1,) x \in (-\infty, -\frac{5}{3}] \cup [1, \infty) - For Q21: x(,2)(5,) x \in (-\infty, 2) \cup (5, \infty)

View Full Solution - Free
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