When 3 times a number is subtracted from 5 the absolute value of the difference is at least 7. Use interval notation to express the set of all numbers that satisfy this condition

Question

math problem

Answer 1

5-3x|>7

5-3x >7

-3x >2

divide by -3, which changes the direction of the inequality

divide or multiply by a negative number will reverse the direction of the inequality

x<-2/3

or change the sign of the expression inside the absolute value sign

-(5x-3x)> 7

-5+3x> 7

add 5 to both sides

3x>7+5

3x>12

divide by 3

x > 12/3

x> 4

x<-2/3 or x>4

x is an element of the interval (-infinity, -2/3] U [4, infinity)

it includes all real numbers except between -2/3 and 4