Solve the inequality and write the solution in interval notation, ｜4x+3｜ -5

Question

Solve the inequality and write the solution in interval notation, ｜4x+3｜> -5

anonymous · Answer

Just make it so the > is an Equal sign it makes it easier

anonymous · Answer

Okay so I've done that and I get an answer of x> 2 and x< 1/2 but the book says its supposed to be graphed as ( negative infinity, infinity). Am I doing something else wrong?

jim_thompson5910 · Answer

The absolute value of any number is nonnegative (ie it's 0 or positive)

so |4x+3| will never be negative and it will always be larger than any negative number

jim_thompson5910 · Answer

so that's why the answer is ( negative infinity, infinity)

it's basically saying: any real number is a solution to ｜4x+3｜> -5

anonymous · Answer

Ohhh okay, wow thank you

jim_thompson5910 · Answer

you're welcome