Answer:
a= -infinity to 3
Step-by-step explanation:
Given
[tex]3 - 7x < 3x - 7[/tex]
[tex]1+2x < a+x[/tex]
Required
Determine the value of a such that the inequality has no solution
Considering the first inequality (Solve for x):
[tex]3 - 7x < 3x - 7[/tex]
Collect Like Terms
[tex]3 + 7 < 3x + 7x[/tex]
[tex]10 < 10x[/tex]
Divide both sides by 10
[tex]1 < x[/tex]
Reorder
[tex]x > 1[/tex]
This means that the least value of x is 2;
Substitute [tex]x=2[/tex] in the second equation
[tex]1+2x < a+x[/tex]
[tex]1 + 2(2) < a + 2[/tex]
[tex]1 + 4 < a + 2[/tex]
[tex]5 < a + 2[/tex]
Collect Like Terms
[tex]5 - 2 < a[/tex]
[tex]3 < a[/tex]
Reorder
[tex]a > 3[/tex]
This means that the least value of a is 4
Hence;
The values of a for which the system has no solution is -infinity to 3
