Solve: 5|x-3|+2>4 The answer has the form: a) (A,B)

trainart1

trainart1

Answered question

2021-11-16

Solve: 5|x3|+2>4
The answer has the form:
a) (A,B)
b) (,A)(B,)
State your solution using interval notation, using whole numbers, proper fractions or improper fractions, like above: ?

Answer & Explanation

Nancy Johnson

Nancy Johnson

Beginner2021-11-17Added 17 answers

Step 1
Consider the given information
5|x3|+2>4
Step 2
Then |x3| open with minus sign when x<3 and open with positive sign when x>3
The solve the inequality for x<3
5(1)(x3)+2>4
5x+15+2>4
5x13
5x<13
x<135
Step 3
Then common value of x from here is
x(,135)
Step 4
Now solve this inequality for x>3 then
5(x3)+2>4
5x15+2>4
5x>4+13
5x>17
x>175
Step 5
Then common value from here is
x(175,)
Step 6
It mean that x belongs to
x(,135)(175,)

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