Solve absolute value inequality. |3x+5|<17

kloseyq

kloseyq

Answered question

2021-12-16

Solve absolute value inequality.
|3x+5|<17

Answer & Explanation

amarantha41

amarantha41

Beginner2021-12-17Added 38 answers

Step 1
The given inequality is |3x + 5 | <17
Apply absolute rule: If |u| < a, a>0  then  -a < u < a
Step 2
Apply the absolute rule, the inequality can be rewritten as,
3x+5>-17 and 3x+5<17
Solve the inequality 3x+5>-17 as follows.
3x+5>-17
3x+5-5>-17-5
3x>-22
3x3223
x223
Step 3
Solve the inequality 3x+5<17 as follows.
3x+5<17
3x+5-5<17-5
3x<12
3x3<123
x<4
Thus, the solution of the inequality is 223<x<4 and in interval notation (223,4)
William Appel

William Appel

Beginner2021-12-18Added 44 answers

Step 1
Given: |3x+5|<17
we know that
if, |x+a|<bb<x+a<b
Step 2
similarly,
-17<3x+5<17
-5-17<3x+5-5<17-5
-22<3x<12
223<3x3<123
223<x<4
hence, solution of given inequality is x(223,4).

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