Question

Which of the following represents the solution to the inequality: x+4<1.5 or 3+x>7?

a) x<-2.5 or x<4
b) x>4 or x<-2.5
c) x<4 and x>-2.5
d) x>4 and x<-2.5

Answer 1

The inequality 'x+4<1.5 or 3+x>7' is solved by isolating x in each part separately. The solution is 'x < -2.5 or x > 4', corresponding to option b).

Step-by-step explanation:

The solution to the given inequality problem 'x+4<1.5 or 3+x>7' needs to be addressed by solving each part of the inequality separately.

For the first part of the inequality 'x+4<1.5', subtract 4 from both sides to isolate 'x':

• x < 1.5 - 4
• x < -2.5

For the second part of the inequality '3+x>7', add '-3' to both sides to isolate 'x':

• x > 7 - 3
• x > 4

Therefore, the solution to the inequality is 'x<-2.5 or x>4', which matches option b).