Solve the inequality: SQRT (3x - 2)2 < 5
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to solve sqrt ( 3x - 2)^2 < 5
=> (3x - 2)^2 < 25
Now (3x - 2)^2 can be less than 25 if 3x - 2 is less than sqrt 5 or if 3x - 2 is greater than - sqrt 5
This gives two inequalities
3x - 2 < 5
=> 3x < 7
=> x < 7/3
and 3x - 2 > -5
=> 3x > -3
=> x > -3/3
=> x > -1
So we have -1 < x < 7/3
Related Questions
- Solve the inequality (2x-1)(x+2)<0
- 1 Educator Answer
- Solve the inequality `|1/2 x-3| lt= 4`
- 2 Educator Answers
- solve the inequality 7 =< 2x-5 =< 11
- 2 Educator Answers
- solve algebraically 2x +y =2 3x + 2y=5
- 1 Educator Answer
- Solve for x sqrt(2x+5) = sqrt(x+2) + sqrt(2x-3).
- 1 Educator Answer
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given the equation:
sqrt(3x-2)^2 < 5
Now we will rewrite using the absolute value form.
==> l 3x-2 l < 5
Now we will rewrite :
-5 < 3x-2 < 5
Now we will add 2 to both sides.
==> -3 < 3x < 7
Now we will divide by 3.
==> -1 < x < 7/3
Then the answer is: x= ( -1, 7/3).
SQRT(3x-2)*2<5
SQRT(3x-2)<5/2
3x-2 < (2.5)^2
3x < 6.25+2
x < 8.25/3
x < 2.75
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers