Question

The solution set for all real numbers x such that 2x + 3 < 19 and 2x − 3 ≤ -7 is ( , ]. Note: If needed, type “-infinity” for -∞ and “infinity” for ∞. NextReset

Answer 1

2 x + 3 < 19
2 x < 19 - 3
2 x < 16
x < 16 : 2
x < 8 ( or: x ∈ ( - infinity, 8 ) )
Also:
2 x - 3 ≤ - 7
2 x ≤ - 7 + 3
2 x ≤ - 4
x ≤ - 4 : 2
x ≤ - 2 ( or x ∈ ( - infinity, - 2 ] )
( - infinity, 8 ) ∩ ( - infinity, - 2 ] = ( - infinity, - 2 ]
Answer:
The solution set is:  ( - infinity, - 2  ]